Title Dynamics on character varieties (Complex Dynamics andRelated Topics)

Author(s) Cantat, Serge

Citation 数理解析研究所講究録 (2008), 1586: 32-60

Issue Date 2008-04

URL http://hdl.handle.net/2433/81535

Right

Type Departmental Bulletin Paper

Textversion publisher

Kyoto University

Dynamics on character varieties

Serge CantatUniversit\’e de Rennes I

Complex Dynamics and Related Topics

Research Institute for Mathematical Sciences, Kyoto University

September 3-6, 2007

数理解析研究所講究録1586巻 2008年 32-60

$0^{b}$$\zeta_{0\wedge}$ 沖

.$sa\psi r_{A=}^{*}\omega vc\alpha ckf\nu\backslash \{A\epsilon P6L(R_{l}\not\leq\chi_{Z)}r_{i}^{\eta}$

I $\Leftrightarrow n\kappa od(A)\}$

鰍胤 R% $\triangleleft Awk^{\omega}$

$(s_{A_{1}\iota,c_{l}o})$ $X+\eta+\chi b^{\epsilon\approx}\#aa_{*a^{2}Ax*8*C\epsilon*X}$

侮吻m.d. $p_{\alpha\dot{A},}\omega_{\acute{\iota}}\epsilon\mu\circ uS$ $*$ $L$

$l$

$P\mathfrak{B}$ .$I_{W}M$ $mA$ $\cup L_{\infty}$

$l$

$m|IwuA_{(}s_{ai}\}_{\sigma_{(}}.,$ .

. ら騙 $-F_{k},A_{\aleph nc}$ $6^{r}w^{s}1$ $m_{de\prime}$ \sim Mt蒐

qoum$a_{J}r\ovalbox{\tt\small REJECT} 6M$ , $\mathfrak{g}_{rwn_{l}}$ $h^{1}u\mu\nu\iota\alpha wn_{(}3t\alpha dcu_{l}$

$P\dot{t}c\ltimes\iota u$ , h成, $X_{\iota\ovalbox{\tt\small REJECT}}^{\backslash }$

$I$

$J_{6\mathfrak{U}}k/\Re_{\psi\prime n\iota}$ ,「臨 1 $\mathfrak{l}\mathcal{N}t\eta’\varphi$ ,$\searrow$

$\text{ぬ}k_{l^{-}}.$ .

. $Hm\mu_{t}$ $\varpi_{g^{\mathfrak{n}\sim n\dot{q}\zeta;}}$ .

$e_{\ell}4k^{d}l$$\mathcal{D}\text{ん}l\ltimes$

$1$$’.p\grave{m}k\mathfrak{l}\mathfrak{D}\dot{\eta}^{u}\mathcal{M}^{\backslash }1$

$For\text{あ}ml\phi$$1$

$\psi^{b_{i[}A}|$

$s_{\mathfrak{i}}t\%\}$ $s_{\alpha\grave{w}}ck_{1_{l}}^{\backslash }\ldots$

. $bh_{\lambda\backslash }k\backslash \downarrow\triangleleft$

$\backslash \backslash$ 繭\mbox{\boldmath $\omega$} $s\text{ふ_{}5}\text{晶}r$ $o_{P^{c\kappa\theta\pi s^{\nu}}}$

$bW_{l\dot{\mathcal{M}}u}\lambda l$ 鮎一$l$

$\alpha_{\psi}\cdot/$ $\text{興_{}uK}w$$|^{-}.$

.

$.k_{\ovalbox{\tt\small REJECT}}^{:}$ $.F^{;}.\prime ffi^{1}.$ ;$ffi_{\Re:}$

$..f^{:}:$

.

.

$\cdot.\ovalbox{\tt\small REJECT}^{1\cdot:}::\not\in^{:}:::h:’\wedge::M^{:}.’:\cdot:.:$ .$:W^{:}.w..:k_{:}^{:}.\cdot‘ 1_{t},:^{;}\iota R:\ovalbox{\tt\small REJECT}^{::\cdot:}:\cdot:\cdot\prime v’\cdot:::$

.

33

$\mathfrak{H}$ 1 Ttsx $M$ rk $s_{p^{Mc}}$ .

$l$$V_{l}$ $\iota$ 甑

臓 $(.Y_{ 1}$ $r$ 4 $u_{\iota\prime}$ $|$ $\emptyset>$ 営鑑$-$

$t\mu\propto$ $m$ $\#\nu\infty kZ)$

$[d_{1}\mu]\underline{\sim}$ $\ell pl.|p\cdot\uparrow$$m\alpha bmh_{\Gamma A}$

$\alpha rwlh$ $\psi^{A\kappa}$ .”..

$\bullet$$s_{4}$ , A $\wp r^{mem}$ Ar&

$\pi_{4}[*)\Leftrightarrow$ $\langle\bigwedge_{l}l,$ $v_{l}S$ $\backslash d_{\beta}V\int\bullet\iota>$

$\sim-$ $F_{3}$ $\mathfrak{c}\triangleright r^{\nu}\dagger d^{\gamma wkS})$

’ $\iota_{\xi}$$X\bullet\tau_{1}$ $r$ $\_{i}$ $u$ A $\zeta X$ ) $–rightarrow A\alpha-f40$ .

$W$ $B$ $(: V_{t}(X)arrow PSL[I_{\iota}R)$ $rIsm^{*}(\mathfrak{D})$

A $M$ $C^{[n_{t}(X))}$ $\grave{\mu}\alpha$ M.et $Aubm\not\simeq$

$n\iota ts_{t}R)$ $\infty$$\mathcal{D}\int_{(^{(v_{A}(X))}}$

$\simeq\cross$ .$\mu_{\epsilon\nu\iota\bullet vu_{\mathfrak{l}}}$ & $\tau_{u}\infty.\# u*k.4$ $*$ $X$ $A_{u}$ $\lambda d$

$d_{tmm\iota\dagger A}^{\backslash }$ $s$ .$s$ Slnu $V_{4}\zeta X$ ) \‘u $\triangleright$ , $\sim Rs$ $\{\iota V_{4}(X)arrow PSL[2_{1R}\backslash$

cm $u$ $A.fbd$ A $SLli_{lR}$ }.

’

34

$E$ $C$ $Jt+d\mathcal{A}\kappa$$v_{ak\grave{\iota}t}h\iota s$ .

$\bullet$

$*i*_{\Im}t*\}_{\iota}$ $4t2 $|C$)) $r$ $\{\zeta^{1}V_{1}(X)arrow\cdot S\llcorner[l_{\uparrow}C)_{j\{}mpk$.

$n\}$

$\bullet$

. $\lambda(X)-$

$b(n_{\iota}Cx)1St\ell 2_{l}C\backslash )e^{\nwarrow}\nearrow\nearrow S\underline{Lp2_{1}\mathbb{C})}$

$hK*6\alpha m\vdash\iota cMd\grave{A}\$ $SL\{2_{\ell}C)ad-$ $b_{*}$

lnwtm $T\infty$$m^{\backslash }K$ ’

$c_{C^{l}}A)$ $rightarrow$ $A\bullet r\bullet A^{-\iota}$ .

$\bullet$丁沖 $SM$ $s_{i}$ $\backslash$.

A $\overline{\vee}$ $h(l)$ $\iota\bigwedge_{rightarrow}$ $\#$ $(P)$ $\epsilon P$ $hV$ $d_{P}$ $h\zeta\iota)$.鴇葛

$\ltimes$ $(tp)$ 審 $h$$\{\iota r)$ $\sim$ 猛 $k$ $(V^{d})$

$\bullet$

$t^{w\ }$$m_{h}\ *nh$ $w^{h}*\grave{u}vwtm\star$

$\#^{\alpha_{\iota \mathfrak{n}S}}.$ $\cdot$

$m_{I^{l}}\iota$

$*$ a $A_{C1}$$\epsilon l$

$*C\epsilon$ $+D$$t’$ $*$ $a^{\iota}$ $*$

$a_{\lambda^{t}}$ a$w\iota R\backslash$ A $=$

$\phi\iota*$ $\epsilon d$ $6\Leftrightarrow$ $l_{e*a^{\sqrt{}}}$

$\S C$ : $\alpha c*bd$ $d$ $\mathcal{D}$

智 $l-\bullet^{\iota}-f^{e_{-}}c^{t}rightarrow d^{\iota}-\alpha ld$

$\wedge$

$\xi_{1_{bM^{\alpha}}^{\alpha\{\_{t}^{l})\dot{u}}}$ $.-n$$8_{\vee}\mathcal{M}^{\cdot}m\alpha d\mathbb{C}^{*}$

.$m$ $\varphi\$

35

$\Phi^{F}|$:$AA^{\cdot}a\backslash$ $*$ & $m_{\eta f^{19^{M}}}\cdot 6r$

$e$

$ffi4m_{f^{6}}r_{f^{\backslash }}^{AAC\pi_{t}(X))\infty\ \sim*(\mathfrak{n}_{1}(K\backslash _{t}sq2,C))}r_{bv_{t}(x1_{I}SLlf,C])_{l}gehk(\pi_{1}(X\backslash )-e\circ\Xi}.$

.$\bullet$

$M\zeta\pi_{1}\{X$)) $\Leftrightarrow$ $X\mathfrak{n}\mathfrak{n}*Mnvpk’m*\{V^{rightarrow l}t^{l^{t}}j$ ct $e\pi_{I}\alpha)|$

$R\mathfrak{g}fO\eta$ 工WE (Vt $(X)$) decs not a&r $\gamma lX$).

$-\sim$ \sim し $\zeta n_{t}\zeta x|)\iota\Leftrightarrow A\phi\zeta\pi_{1}[X\backslash 11I\mathfrak{n}\mathfrak{n}(V_{1}\zeta\kappa))$$\alpha e,*s$ $\alpha \mathfrak{n}\chi[X)$ .

$\bullet$ $Rrm$ $0A(\pi_{1}(x||$ $\alpha.\mathfrak{n}.A$ $wi\#$ $\ _{wrb}$$\phi rm\not\in\chi$ .

$q$ .

$\S L[l_{t}l$ ) $a$As $\sigma V\iota$

$TM$ 験 n鴻● 5$w1\# C$

$\downarrow$

$P6L[t\iota)\alpha\theta_{S}$

幽魅 $**$$H\epsilon$ $\{[o_{1}o$)} $(0\iota_{l}\sim\dagger 1, (_{\vee}^{1} \circ)\iota \prime\prime(_{\frac{t}{\iota}}\iota|\approx)\}$ a2- 一験 r 4 $T$

$M\alpha\$$\vee_{\underline{R}}*\overline{-}\backslash$

:$B_{m\dot{u}}^{\nu aL[l_{t}l)}.\wedge E\alpha\theta nrc\mathfrak{q}^{r}(\_{h}).\epsilon_{\mathfrak{b}}$ .

36

$\Phi$

$Ad_{W\mu_{\dot{m}}}$ $*$ $S_{A_{}6,C_{t0}}$

$(–$ $rh^{\mathfrak{m}d}.k^{\backslash }\wp_{m\emptyset V}r^{\mathbb{L}_{h8}}.)$

. $S_{l}$ : ($u_{|g_{t^{*)}}}\epsilon S_{A,\epsilon,e,0}$ $rightarrow$ $(-\approx-t^{a*A}$ /9, $\iota)$

$s_{S}$: $(\sim‘ \mathfrak{g}’\approx\urcorner ls_{\alpha_{\iota}\iota,c\mathfrak{D}}‘ rightarrow p_{1,-\theta^{-3**S}}, P)$

$S_{1}$$l$. $(Y_{11\iota^{t)}}\epsilon S_{A,f,C,D}.rightarrow (x_{\#},’-\simrightarrow\approx \mathfrak{g}+C)$

’ 荻 $[u_{fw^{M\propto 1}}l\backslash .$ $mr$ $r_{l}^{r}$ 。山 $m$ $S_{A_{1}6}$, $c_{\ell \mathcal{D}}$ .It 加暢 加 $AA(X]$ $R\mathfrak{n}M$ $w\iota A\angle s_{\sim},$

$s_{1},$ $s_{\iota>}$ .

$\bullet.’ S_{\mathfrak{n}_{\}}s_{l_{1}}$

$\alpha r\sim M\backslash$

: $h|\backslash \backslash$

$(_{0}^{\sim 1}(_{l}^{t}(_{0}^{t}$ $-to_{O}-1^{\backslash }lI$

$\}_{r^{\alpha r_{a}^{*}}}^{M3\ovalbox{\tt\small REJECT}\grave{\backslash }\emptyset}.$

,

$\text{嶺}K$ : $4\epsilon s_{\partial^{\bullet b_{1}}}$$*\gamma u\mu b$

$fs_{t\# t^{*\uparrow}}b$ $(\cdot 2..t\cdot\uparrow^{s\iota\iota*\iota^{\iota}}cdot C_{\wedge,l}|(-1-\gamma**C)*k_{t}$

$-s$ 七\iota 亀 $*a^{\iota_{f’}}C_{1}\prime I$$-aarrow\psi tC1_{1}\overline{.}$

37

.oe T鮎 $\alpha_{b_{C}}|.$ .

$cRA$ $A_{t}8_{t}C_{t}\Phi-$ $ot\theta 0t’ 4$ , $M$ $S\grave{\ovalbox{\tt\small REJECT}}\nu\sim s_{\#}$

$\iota^{\iota}s\eta^{\iota_{*\text{曇^{}S}\text{十}}}n^{p}=4$

. 伽麟砲$\iota$ : $C^{*}uC^{*}rightarrow C^{1}*C^{*}$ , 2 $[u_{1} \nu)\Leftrightarrow(\frac{\iota}{k} \dagger\frac{t}{v})$

’

$Y\aleph$

$\{$

$.rt\oplus_{l}vtrn)$

$|:.$’

$u_{\theta a*}$ $\alpha’ h\dot{w}_{\Psi}*c\dot{u}\ R.hS_{A_{1}6_{1}c_{\iota^{\phi}}}$.

A. 4 $*\psi^{u}$.

. $*K$ $Wk$ & $Ac\mathcal{M}M_{\dot{4}}b9_{e}$

. $vk\#W$ 6 $l(1,\mathbb{Z}|a*nC^{l}.xC^{k}b.9bnm\sim^{4}$

$t\nu\sim\triangleright mkn\iota 1$

$n_{s}l_{\epsilon}^{\wedge}d{}^{t}1t(\mu,v)eC^{l}\kappa C^{l}\mapsto(a^{Q}v^{\#}\mu^{C}v^{d}]l$

$*$ $P\xi tl2_{p}Z)$ $\alpha hn$ $g_{c}$ % $rh^{\mathfrak{n}m^{\backslash }A}d\grave{\iota}\rho\mu_{0\prime\rho}\ \cdot\downarrow u$

$\Phi$ $\Gamma_{1^{k}}$ $\infty\ \sim S_{C}$ : & $bhA.wa\epsilon hnt1$.

. $a_{m}tk$ : $W’.u$ A西 $C_{t}D_{P}$ $O_{\mathfrak{l}}O,O$ , 向$\mathfrak{l}$

甑 $q_{R\alpha}$ $*$ $r_{2^{1}}$ $\dot{\mathcal{M}}$ $e_{\grave{w}*rd\not\in d^{\phi}}$ $b*$

$hmA.w$ 偽一\sim $e\mathfrak{n}$ $C$ 匿 $C$ :$\alpha$ ae $m$ $C^{l}xC$ 質 $rightarrow$ $S_{C}$

$S$

‘$k$

$w_{t}\eta$ $\eta st\ell\kappa_{f^{b}}$ $\sim(_{\sim_{\tilde{r}}}^{1}.s, -W.\frac{t}{v}, .\text{執}\sim.,\wedge l\dot{\vee}\dagger, )$

レ\sim $h\dot{w}d$

38

$‘ ffl^{:}$

$AA_{R}^{\cdot}4$ $r_{I}\# k\dot{\mathcal{M}}\mathfrak{b}^{\aleph\wedge}.b$ (I)

$\Gamma_{l^{F}}c?\xi$晴津) $=R(\mathcal{D}]$

ら鹿架 e\rho 架蛎泌 $\not\simeq$ 艦

$m_{r}\psi D\theta^{iw}b:\wp$ .

. $arrow r\Leftrightarrow k.\oint$. ム $*S$ eonh.& $\xi\epsilon_{-}P^{\bullet}(C)$ .

$m$ $S$ $S_{*}4\grave{w}b^{\backslash }\dot{\wedge}\mathfrak{h}\backslash$.$I_{\alpha}d(s_{\alpha})\overline{rightarrow}[rr_{\sim\dagger}$

$\text{つ_{}l}$$\dot{u}\iota tw\mathfrak{n}$ 勧禍\mbox{\boldmath $\pi$} $nv_{l}$

$o_{7^{\mathcal{M}}}o_{e^{m}}\dot{m}vw|.d$ .

工 $\lambda$

$l_{\theta\approx}$ ) 魯 $l^{v_{j}}J$

$Ml)\tilde{r}^{1}1^{\cdot}rightarrow\backslash \{\nu_{l}\}$

$hd\mathcal{D}_{1}$へ $v_{l}$

$\mathcal{D}_{1}\dot{u}\dot{m}vut^{*}d$ .

39

$\Phi$.$A\mathcal{M}^{\cdot}$

$*$ $\Gamma_{f}^{*}$

$A\dot{w}b^{\grave{b}}h$ $tu)$

$u$ $Y$ 曝 $\Gamma_{k}^{*}$ : $Y\varpi r*\rho dsk$ 噸 $\dot{u}mb\#\Phi$$\alpha$

$rrn_{\psi}d\iota k\alpha$ $i_{X}R$ $\mathcal{M}m\iota b_{X}$ .$\lambda[\forall\dagger$ : 瞥 $\iota_{u}\mu$ $/\Psi^{\nu A[}\forall\gamma$ .$Y^{\dot{w}}$ 加戯 $k$ & $m\nu b\text{ぬ}e4^{\cdot}$ A $(\gamma)\geq|$

$Y$崩 $\mathcal{M}^{\backslash }kk$ $\int^{u\theta h}$

. il $\triangleleft(i)\bullet\int$$\mathcal{M}$ $\gamma\approx(_{0}^{\iota}s\alpha\circ|)$

$Y^{\grave{\mu}\mu^{\backslash }kk}$ A $\text{一}\mu\text{。}$ $duw\iota\kappa$ .$\underline{Fd}$ : $\ovalbox{\tt\small REJECT}_{\dot{\sim}r}\$ $4>$ $\eta.\eta_{k}^{w}$ $\alpha\triangleright$

$s_{*},$$s_{\theta}*S_{f}$

$\psi^{M}$.

$l-$) $m$ $ihu$ $\#$

$s_{a^{\bullet}}s_{9}$

$\delta r$

$s_{9^{oS_{2}}}$$\alpha$ $S_{u}eS_{t}$ .

.’

$r_{t}$

40

% $b\eta\%^{A}\eta\dot{\mu}$ $A\alpha ps_{A,9,c_{\iota}v)_{J}}\#\dot{u}$

$**w$ 級.

$\ovalbox{\tt\small REJECT} h$ : $\lambda\{11$ $:*$ .$ $(\gamma)^{-_{k}^{1}}$ $b\eta$ $k_{f1}$

$*4$ $M$ $p^{h}$ 勲 $\text{\‘{u}}$&d $*$ $Y^{\xi}$「$p^{*}$ .

41

$\otimes$

’ $J_{\sim} \mathcal{H}^{\underline{4}}(M\int_{l\iota,}u\mu_{l\mathfrak{D}_{1\ _{i}}} \cdot\Re^{u\mathcal{M}}jb\searrow RkS\mathfrak{t}\sigma\eta\}$

. $f’.Srightarrow S$ $A$$t_{lrdo\alpha d}$

$\triangleright_{W1}\mu_{A\dot{r}}4$ $\bullet$

$m$ p呼祷べ \sim 西.’ $hp(l’.)nhd[1)\Leftrightarrow f/$ $\gamma^{t}(IuJ)\Leftrightarrow Ld[1|$

$fl \mathcal{M}\sqrt{}^{-||\bullet}I_{b}d\cdot[\int.,)$

$\bullet\oint^{*}:$ $H^{a}[s,z)arrow$ #’と S,Z)$2(\theta^{*})\epsilon$ $A_{n}W$ $//[1^{r}r\Uparrow/Jm$

$marrow*\sim$ .

$M$ $A4^{l\ell\}}--$ $h(\triangleleft(1^{*})|$ .$\bullet rMdcr$ : $HcS$

$A_{\theta t\theta)}--$

$h^{\mathfrak{n}\text{輌}=\%}$ かゑ $\sim$ :

$A_{4^{\downarrow t1}}\Leftrightarrow$ $b(al\not\in|)$

1

42

$\backslash \cdot$ MWmd $k^{m}$ A $\dot{\mathcal{M}}\int\backslash \wedge\backslash h$ (I)

$\bullet$

$\#\iota$ ae $|,$ $\bulletrightarrow$ $ae$; a $r^{\vee\infty}$$d$ $u_{m\sim r}\ \cdot C$ $\infty$ $\mapsto$

$\$$or\backslash ^{\iota}*^{V\backslash }\cdot$

Assw $\infty$$\oint$

$C\delta\backslash f\nu\alpha k$ $b*$ mes $rightarrow$ $(’,$ $\bullet)’$.$l$ $(\{r\cdot\epsilon\})$ $-$ $f( \{\theta^{\iota}o\int)$ – $p9,$ $\circ$).

尤 $d_{r}$ :$V_{1}(\not\subset\# 2\iota t5^{C^{*})}\simarrow Z^{a}v_{t}(C^{1_{\wedge}}C^{*})$

& $\mu_{\iota}$ 伽, $m_{\psi}hAdh$ $\oint$ :

$t_{r}$ $(_{\iota^{\rho}})$ $=$ $(_{e}^{\wedge} \int)(_{f\prime}^{f}t)$ ノ $\ l_{\epsilon d}^{\alpha}{}^{t}l^{p^{*}}-\mathfrak{l}$

$v^{\backslash }.\iota lnl^{\ovalbox{\tt\small REJECT}}\ u\prime hr^{\ulcorner}\wedge\nu r\iota)$ : 3 $\alpha\Psi^{m}\# A*_{mo\nu\rho}\ _{c}$

$;^{Mr^{\text{ム}}}x_{\ell^{\backslash }\cdot\ell}.a\sim ju_{\oint f}\ k\prime u_{1t)-f)}\Psi:a^{l},\bullet-C_{\iota}^{\bullet}o\ovalbox{\tt\small REJECT} A,u_{\theta^{\iota_{l}e}\phi^{d}}[(\alpha_{13)^{[_{\epsilon l})})_{\sim;[\Psi[\tau,1^{1)}}}\sim lz^{\wedge}\sim$

$\bullet$ 3 $\kappa_{\mathfrak{t}}\epsilon$ 果 L(2,z’\urcorner )

$\{u_{t}v)\sim$$\dot{\zeta}u_{t}*\iota^{u_{\text{《}}}$

43

$\text{韈}\Phi$ $NrM$ $\Psi^{nSkm}^{*}\#^{\dot{b}}\%$ $\Psi]$

’$h_{1}\rho u^{\backslash }.h\alpha$ . $\llcorner\phi A_{1}8,C_{t}b\epsilon C$ ,

は $t\backslash$ 娠 $9_{1}Luu_{\#}r_{*}^{r}$ .$uf:^{s_{\iota_{t}\iota c_{\iota \mathfrak{D}}}}.‘arrow s_{t_{1}8,C_{1\triangleright}}k\ u_{r\iota^{\gamma}p}u_{n\iota}$

$rr*m^{\iota}\iota^{n}$ .

MAuw 1\sim た $Au^{*}\forall u$b&nd $I_{\lambda}d1*I\kappa d\ell^{1}.$ .

$\zeta\grave{\iota})$ $ar_{1}$ a $Ar\triangleleft\dot{w}^{+}\iota_{\psi}$ mト rtx $w’|k$ $>,$ $Orkrt*$$wk.4\dot{u}$ Rj鴫戚為 $*Jt$ .

$(\ddot{\wedge})$ 3 $\Psi t\{C^{\iota}o1’-l\overline{S_{A,\mathfrak{g}\rho}}$,。/

$l\backslash d\{^{-\mathfrak{l}}I$ a $r^{\nu m}$

4 $M_{0\vee\ }$. $A.*\circ n*r^{\omega_{b}}$ $w4K$$\oint(\Psi(\wedge v)\dagger\backslash =$ $\Psi((u_{1}*1^{N}1)$

$Rk_{f}$ $\forall n\epsilon$ $PSL[1_{\iota}Z$ ) 3 $W$ \sim \sim u収 $\geq 0$ $a,*h.e\delta$

$nA$ $\aleph.*$ $\dagger\triangleleft\dot{u}c\sigma$ 隔塾 河 億 $\dot{u}$ ’S沖 t4 $\text{【}$)..

$k$W品– &A $\alpha b\{\S\backslash$.

$\omega$$(\backslash _{t}q_{t}\not\in)$ a $S_{A_{t}8,C_{t}\infty}\zeta C$). $h\iota\iota mR$ 甑 $\mu_{ud}$

幹鷺 $*$ $(\backslash |9|a)$ 心 $M$ $bmlm$$f^{\alpha}(a_{\iota 9t^{t)}}$

屑–\div鱒$Ld[1^{-t}]$

$\mathcal{M}$ 繍 1 $\varphi_{t}*$ $A_{b}.f$ 論 $w\ovalbox{\tt\small REJECT}$ $\ \mu$ :

$q_{\underline{m}n}$ $a:(\alpha_{t\oint\downarrow*)\partial}$ $marrow*\cdot\sim\ ^{\backslash }b$

$\frac{1}{\sim\iota}r*||i^{r}(\tau_{\uparrow f\dagger}\epsilon)\#$

[. $m$.

犠 $\zeta_{2}{}^{t}ibackslash \t$ $*$ $\downarrow\sim|^{a}*$ [9 $t^{\iota_{2}}\downarrow 3|^{t}$

44

$\otimes$$g_{tW\aleph}\triangleleft\ovalbox{\tt\small REJECT}\ovalbox{\tt\small REJECT}*I\iota A(8^{r}.1$

$r$ uぶ h $\prec$ $mm_{\phi t}\triangleleft$ $\text{工耐}(_{\omega}f^{-t})$ :

$\iota IL^{s}(\iota_{\backslash }l\{p^{-c}))$

$\simeq fm\epsilon s_{s_{\downarrow\dagger}c_{8}p}$, $\zeta C\uparrow i$

$\iota^{\wedge}(\sim)\alpha\neg\sim L4[l^{-\iota})fs\infty$

$n[Ld[\iota^{-1}|)$

$\Leftrightarrow t\sim\iota\overline{S_{f_{\iota}\emptyset\ell_{1}\mathfrak{n}}}(C)j$

$t^{\alpha}(\propto|\supset\overline{\wedge\triangleleft}-^{Ld}(l^{1}.)\int$

$\ovalbox{\tt\small REJECT}^{k}\zeta N\zeta)\Leftrightarrow\{(\bigwedge_{l^{\psi}})\epsilon ae^{s_{t}}C^{*}$

1珂 1 $<[mt^{s_{l\#)}}1_{)}|$

.$m_{\iota}$ 」曳 $(_{stl)}’)\sim$ A $\iota t$ ) $r_{sld1}^{\dagger})$

$\downarrow,\backslash .l$ . $4(f|t_{1}$ 晩 $*e$ $d$ 椀 $\eta^{lr}.p_{i\text{伽}4}$, $d$ $N\ell$

$mur$.$b$ & $u^{\backslash }\psi^{V}A$ a $l\#$ ) $[$

$\Psi$ $\ell n.bd\iota$ A $a$ $m,\mu_{\backslash }c$

ら dW$gk$ $A^{*}$ $(\aleph\ell|\sim A^{*}(ldl.f^{-1}))$ .

45

の $xk^{\backslash }\propto$ $\mathcal{M}$ $\mathcal{M}$ ’け鰍価.

$x_{\}$ $h$ $*\backslash :\}$ . $4$ $\sim$ $w$ $m$ $l$ $s_{\iota_{\iota}\epsilon_{t}}\epsilon_{\iota}o$ $\zeta\Phi)$$\ovalbox{\tt\small REJECT}$

.$\sim$

.$\sim$ , 風\sim

$a^{r}\$$t^{\alpha}$

$[\sim)\sim \text{角}\neg*parrow I\mathfrak{n}\{(1^{r})$$arrow$ $/\forall\downarrow sr^{l}\beta_{C}df^{\iota}.)$

$\infty$ $f^{r}l\sim|$ $arrow$ $Idlf)$ $\infty$ $m$ $ea^{\iota}(1d1)$$\simarrow-\infty$

$\bullet$

$N\#*_{r\prime\}$ . – $\iota\theta**^{\vee}$ $s\theta s-$

. $K^{*}[f$ ) 蜜 $.\{m$ $\int$ 翫 $*wa\kappa dn1_{1\star}.\# k\eta$ あ $bown\mathcal{M}$ }蜜 $m\text{い}M^{\text{赫}}4$ $A^{l}\zeta Mf\cdot,$ )

$K^{-}(\{)$ $\{lV\mathfrak{n}$ 1 廠 』仇 Aw偽 $d$$rL_{1\succ}^{\backslash }\dot{u}bm_{J}$

夏 $t8$ ) $K^{*}q$ ) $\theta$ $K^{-}P\ell$ )

$l’$ $\tau*ff)P$ り $K^{*}[f)$ $T^{-}(\not\in)\approx 3K^{-}(\beta)$

了\iota $t$ } 篭 $3^{*}(1)\mathfrak{a}J^{-}\{1$ ) こ a $K[I)$

フ $\bullet$

$t\{\}$ A4 $kd\propto A\iota Rr^{u\grave{\iota}\Leftrightarrow\star^{\backslash }c}pM$

イ 1 $\cdot$

.

$-\Xi t\#^{A}mM-$

$\bullet$ $T^{*}1\overline{rightarrow}$ $dd^{t}6_{\ell}^{*}$ 禍衣 o

$\tau_{1^{-}}$ a $dd^{g}6_{\overline{\{}}$ $M$

$\bullet$

$\mu_{f}$呂 $\text{丁_{}\beta}^{*}$ A $Ti$

$G_{l}^{+}$伽、$\Leftrightarrow$

-\sim \rightarrow 今\tilde $\frac{\iota}{\#}\{)^{b}b^{[1}fh)\#$

$\epsilon_{1^{\vee}}(\sim\backslash -\ \alpha--\bullet\frac{1}{aq}r*\# l^{\wedge}(\alpha\}|$

$X.\int$ $1\{$ $\mathcal{M}T\overline{f}$$\alpha r\iota$ $mW^{\backslash }d$ $wre4\theta 1M$

麗 $\#$’

$m$ $\oint\cdot J^{\backslash }\wedge V\dot{w}\ovalbox{\tt\small REJECT}$ 価鵡

46

$\otimes M\ovalbox{\tt\small REJECT} k_{\backslash }^{gv\mathfrak{n}}m_{1}f\triangleright klf_{*\iota*n}^{r_{\iota}r\cdot v,t_{\iota}wMFr\backslash us:.\psi|A_{1}t\iota_{\Psi\}}} d6’x_{u_{1}}\eta_{\aleph Mm\aleph wr}^{\backslash }h^{c}.\%_{\iota}^{R\dot{W}Q}\backslash \cdot ht_{\iota}s_{t}\ldots)$

吟町ゑ $w\ovalbox{\tt\small REJECT}$ &*d.$\bullet$

$\triangleright\iota$必輪 $W^{\backslash }$ $t\cdot\grave{\infty}vcl\alpha dP^{\nu\cdot 04\alpha t_{\backslash }l\backslash b_{l}}$

. $m\epsilon m$

$W\backslash *$

$m\backslash \infty\backslash uh_{0}’\#\backslash$.$l$

$A_{\mu}(\theta)rA_{4^{[f)}}\Leftrightarrow*9(\not\in)$

$\bullet$ $\tau km*$ $p^{y_{|\ovalbox{\tt\small REJECT}\epsilon}}..r^{M}*$ $f4$ $P^{u_{1\bullet}^{\backslash }d}n\grave{\ovalbox{\tt\small REJECT}}$

$\#^{uh}$.

$\mathfrak{c}_{lw\propto:\sim b^{*}- u\iota R\alpha}1u\gamma^{4_{i\infty\backslash }}\#\nu m\{r1\approx$ A $l1)^{N}$ .$M**\ovalbox{\tt\small REJECT}$ an $*\text{冒}b\text{設_{}\zeta}$ $Aau4\mu$ .

$\frac{1}{1l}t)^{\aleph}\alpha e\simeq_{u\sim}$

,$\kappa)g_{t\alpha c_{\alpha}}$

.$arrow Narrow\neq\triangleright\mu_{f}$

$Wu$. $*$ Py $li\prime^{N\}\overline{\sim}}$.

$\alpha$$.l^{*!}.fSt$ $u\grave{\backslash }\mathfrak{n}u^{\backslash }duw|.\#_{t}\ A_{\Psi\mu*\mu_{1}}$ .$b\Psi^{\iota^{*}\sigma\ ^{\backslash }uM}r^{rdJ\grave{l}\grave{u}\ A}m^{F}\#\mu_{1}$ .$z_{f}$ $rp*kltr^{\ell r^{\backslash }\iota Ac}..\cdot J\bullet du_{\rho\#}u$

47

$ae$

$l$ $X \int$$r$ 為 仇 $\lambda\alpha uA$

$P^{u1\epsilon A’c}\mu\prec$ $ 1$\#\wedge$

W勘 $tr$) $k$ $r^{wwh_{ia}d}$ $\text{し_{}9}$ $c_{:}$

$B$ $g$ $ $C$$\vec{u}$

$s_{A_{8}\text{鍋}}{}_{\mathcal{D}}C\text{の}$

$\grave{m}*$$f$ $A\grave{m}\dot{r}^{d\kappa}./$ ? [$0)\Leftrightarrow Pm$ ? と¢)魯 $W^{\alpha}(\rho)$

厩 $De$. $\mathbb{C}$ 沖\epsilon $h\grave{m}\star$ 0む=h$l$! 七 $\chi$ ら c $\propto$

$m$ $\mathcal{M}\beta*\mathfrak{R}^{\phi ck}$ $k^{4^{\backslash }\alpha}o\mathfrak{n}$ : $(\Psi)\infty.\#$

$\alpha t\alpha)>$ 。 $\infty$ 俳。 $*$ 9 $\Phi$ .Let $[\zeta l\Phi|]$ $k$ $kC’ wrd*\dot{u}*\eta\prime d\dot{\alpha}uf^{C\Phi})$ :

$\langle$ [\S \mbox{\boldmath $\zeta$}\Phi )] $|d\alpha I-k\wedge>=$ $\int_{\Phi}$$f^{r_{4}}$ .,

$vb$$\frac{1}{a\iota 1}|^{r}$

$1^{Jr},(\gamma$ . $[f^{(p)}J)\overline{\alpha-\infty}^{c\backslash T_{f}^{rightarrow}}$

’ $b$ $\{$ $\dot{\#}$ $ra$ $P^{w\iota tV1}\mathfrak{l}$wt $\infty$

へ:\mbox{\boldmath $\pi$} $(\ltimes[f))-rightarrow$

葛

$Lb.\vee(K^{*}(*)\backslash$

工-1\sim Y $(K^{\cdot}(1))$

$\iota_{m\cup}\eta^{g_{\wedge}}$ $M$$4$ $s_{\bigwedge_{1}1_{1}C,b}$ (C) .

48

$\mathfrak{H}$ T沖 $\alpha_{w_{\dot{b}}}arrow F_{\lambda A}h_{1}\backslash m$ $s_{p^{u\{L}}$ .

果 誠 $f_{P^{W}}$ . ( $\triangleright$ 甑 $W\aleph AW^{\iota\dagger wd}\sim u\sim$).

. $a_{uA\aleph}\text{転}A_{b\ovalbox{\tt\small REJECT}}$.

49

$\ovalbox{\tt\small REJECT}$ $8u_{S}$ $\mathcal{P}uwfviu" A_{M1}’$

$\frac{Q\ulcorner}{Q\ulcorner}\dot{u}\underline{rightarrow}DFw,\eta^{\text{軸}}-$

$A4bd\not\leq$ $S$ (ae),$-\{\iota p1$’fl\rightarrow SL提,c) 心\alpha 古 $*^{\backslash }\kappa\mu\}$

轡$e_{\alpha\}$ $?w\alpha_{1}wf\gamma ig*\cdot\alpha$ .$t^{l}u$ $hm\propto$

$w^{A_{-}\mathcal{M}}+_{\bullet ru}/W\iota’k$ &\eta r\alpha ;h $\alpha idA\dot{m}$ .$m\mathcal{E}^{\gamma_{\}}1$ 窪嚇を

$l$

1諜 $\mathfrak{c}\tau’)$ 聖 $H^{-}\cdot$ .$\ovalbox{\tt\small REJECT}_{1}’ l\}_{1}\iota*n$ $H^{\dagger}\mathcal{M}w^{\iotarightarrow}$

$u-\zeta\Re$ 38.$m$ $\backslash$. $E^{*}xH^{-}rightarrow$ QF $\alpha M_{\alpha_{f}}k_{\iota}$.

$\lfloor A\ovalbox{\tt\small REJECT} mJ\mathfrak{n}AM\forall\#\epsilon 6Wl_{l}2^{\wedge})\Leftrightarrow bCG\zeta T,)\forall\zeta X_{I}\forall\backslash \epsilon H^{*}H^{arrow}.Ta^{\backslash }4\zeta T_{1}|_{X}Tu^{\backslash }d\zeta T_{t}’))$

$B\alpha(I^{\ell_{X)_{J}}}t\iota))\epsilon$ $\#(8_{\ell tS}Cx,\forall))$

$m^{\backslash }\infty.$ & $\mathfrak{R}\eta^{du}$ & $\alpha*_{\alpha A}$ $*MC6(T_{4})$ m酬

$\dagger b$

。$bT\epsilon$ 閉� $W^{-}/$ 馨, $\overline{\vee}\overline{-}a\}$

1孟 $(T_{\iota}|$

$k$ & $\alpha \mathbb{A}$.

$d$ ’ら $1\{8_{j}l$ ) $u$ $S\zeta \text{沢}$ ) 八 $\mathfrak{c}\kappa^{l})’$ .

50

$.g_{1}$.$\mathfrak{D}\eta^{uma}$

.$\alpha$

$\pi_{F}$

$r$ 丁 HH $\zeta.A_{i}u*J$

$\ovalbox{\tt\small REJECT} m\sim r^{\nu\alpha Ar_{5_{1}l|}d\alpha} ffinw\frac{\alpha}{\aleph^{*}xE^{-}}\circ\alpha*uds\text{岬}k\backslash \{p|\zeta R)\}L_{C}+wmwd\mathfrak{D}F\infty$

.

$\Im^{l}\zeta\aleph_{X}^{*}\aleph^{rightarrow)}\approx$ $\circ \mathfrak{c}*m_{xW)\backslash \{(u_{l}x)_{i}\sim\epsilon P^{1}p\Re\rangle\}}$

51

$\ovalbox{\tt\small REJECT}$

$N_{\grave{t}}\omega$ 0Y礁

争 $R$$\alpha r\dagger\#^{\aleph}.$

. $\{\theta_{t}O_{j}\phi)$

$TL$ $\ovalbox{\tt\small REJECT}\zeta\phi_{1}\Phi,Q)$ $\epsilon S$$\grave{\mu}\propto\iota;\kappa P^{r\#}$

$\zeta S)$ $x^{a}+\eta^{a}+a^{z}=\infty\#^{\text{ぞ}}$ .It cerruponds $k$ & $*\dot{u}b$ $r\varphi grbMC_{\bullet}^{\iota}F_{a}arrow S\llcorner(P,\not\subset)$

婦 $b_{\theta}’$.$\zeta_{l}$ ( $\aleph|\overline{rightarrow}$

$l_{\dot{k}}^{O}o\dot{\sim}$ ) /$p_{\bullet}(\rho)\bullet$ $(_{1}^{O}-|0]$ .

の

嘱$\S_{R^{4}}$ $(8\bullet wh.tA)\backslash$. 3 $\alpha\ovalbox{\tt\small REJECT}^{\text{し_{一}}\text{心}}$ 肌 $d$ 甑

$\propto\grave{\backslash }\varphi\searrow$ ( $(.\theta_{l}o_{l}O)e\mathfrak{U}$ C- $s[0\gamma$) m庶也硫

$\eta_{m}e$ 妖 $hC\zeta(v_{\alpha})\bullet m$ a $(o_{l}0_{1}0$).

52

$\Phi$

$(\theta_{l}\phi,\#)e$ $k(1]$ $\rho_{\kappa 4\mu^{\psi}}$ .

’ $I\#$ $(_{Q_{1}o_{\iota}\circ\backslash }e.Lb(k. [\iota)|=I_{\alpha}b[K[f)|1\kappa$

$\#\grave{\mathcal{M}}$ .Ar.R 誌も $0\nu t\psi^{\backslash }4$

$\bullet$

$bk$$\mathfrak{D}f_{1ut^{0_{t}t)}}$ 編 $\mu b\alpha dw$ $\mathcal{M}\#\dot{u}$麟

$P^{u_{\grave{\iota}}A^{\backslash }c}$ I $k$ $(0_{1}0_{1}0)l\iota k\mathfrak{c}_{K^{\sim}}\varphi])$ ..) $(0_{1}0_{t}0)e\mathfrak{g}_{K}-\#)$ .

$e$

$\infty$ $W^{S}$ ( $|\grave{\mu}$ $M$ ふも $c-q$ )$\mathfrak{l}$

$W^{S}(?]$

$h$ $\eta u$ 厨 $u$ .

53

$‘\otimes$$\mathbb{E}m\#$ $\ell\alpha b_{1\mu}\lambda A_{0\eta}T_{4})$

. $m$ 瓶 $ta\ltimes k^{\backslash }b.n$

$\lambda\cdot C$ . $\zeta^{\zeta s} b]^{1}\overline{-}$ 期

1. $u\mu jMN$

. Wt $m$ $J\#p$ $T_{\wedge^{\backslash }}R^{\backslash }.\ u_{\iota},+w$.

$*\dot{A}t\alpha\prime \mathfrak{n}$

$A\mu_{m}m$画甑 $\text{昨し_{}i\mu}$.

$w_{1}$ .

. 吋 w 「船 $m_{\partial l}\triangleleft$ $\sim^{a_{*}}9^{\iota_{*8^{C}-\approx y\Leftrightarrow r}}$ a.

54

.$,

REAL vu$svs$$Co\aleph PL\epsilon\gamma$ $\mathfrak{D}_{\phi^{\mathfrak{n}MCS}}$

1軸 $l*At\wedge$ い血 $mP^{uM}$ $.r4$$\alpha^{\backslash }*x^{\iota}*a^{\iota}\text{・箆架}$ $+\Phi$ $(S_{\theta})$

. $To_{f^{O}*a}*$ $s_{n}\zeta Rtl$ De $R$ $(8\iota \mathfrak{n}\iota d\iota*o_{l}Q_{0}!dr\alpha u\}$

ぐ夕 $\triangleleft$ .夕ヘ $e$

夕

$\mathcal{O}Q$$\sigma\varphi$ $\theta$ $Q$

$km\lrcorner$ A ヤム\iota $\ovalbox{\tt\small REJECT}$

$” m_{l}$ $R$$\prime v_{lI\wedge}bW$

55

$\oplus$

$\ovalbox{\tt\small REJECT}_{L*\text{《}\ \ dm\phi\infty\not\leq m\alpha d\iota_{9Y}}\ovalbox{\tt\small REJECT}\iota_{\# mR.fl}^{t}tIS_{\bigwedge_{\iota^{f,C_{1\triangleright}}}}(R1\grave{\ovalbox{\tt\small REJECT}}muer_{R}^{\iota}khr_{Hr}^{u}u_{c}^{Al}\phi A_{1}t_{l}c\nu^{\zeta R)_{\dot{\prime}}(s_{\eta r\mu f)<4}}\mu\beta\dot{u}k\mu w_{1\#\hslash hk^{\backslash }\ _{W^{mulR}}}^{\backslash }r\alpha r^{\ell\oint_{-\ovalbox{\tt\small REJECT}}^{S}} u^{v}\ovalbox{\tt\small REJECT}^{\wedge}\ \ovalbox{\tt\small REJECT} A_{1}8,C_{t}DCtcA\iota 8rC_{t}4^{wmf*S}\cdot.\cdot$

$Sk\}A4$甑 $r^{r}\triangleleft$ . (Nも $A_{t}8_{t}C_{t}\mathfrak{D}-o_{\ell}o_{t}o_{\ell}\triangleright$ )

( $A_{hIWtt}\epsilon_{\iota}w^{kn}$ $\iota_{t}$ X $wu_{\wedge}k^{\backslash }$ ).

56

の $\sigma \mathfrak{b}_{\epsilon}+4$

$*$ $A$ $\not\simeq r\text{イ}\not\simeq$ A エ.

–

57

$\theta$.$SWA\triangleleft$ $\ \uparrow \mathcal{H}*hm_{m}$ $r$

$Eh\eta\int$ .. て $b^{\phi}hm$ $w\ell$ km

$\mathcal{A}\eta(f_{R})\leq 4_{\phi lfae)}\uparrow=kb[t))$

$N\omega Vu*\cdot\infty$

$\triangleleft$ \iota w\alpha $山-uLm.

$\bullet$

$\text{丁}k$ 勉. $A$ $k^{ovn}$ \nu 山 $m$ $R$ $g_{mb^{l}S}$

$\grave{\lambda}h\ovalbox{\tt\small REJECT}^{\backslash }b^{l}$.ム洗 (四 $L$ , wこ $rm\alpha\nu k$

$u\dot{a}\}$ 9 $\epsilon u$ $u$ 改$\Psi^{\epsilon\prime_{tc}}\backslash$

$*$ $t\xi \mathcal{T}_{4}\zeta*^{u})tr^{b})$

也

$\ \uparrow^{f^{\text{亀}}}$

$\theta_{\hslash}^{N}[p]$$\sim$

$r_{C1\prime 1^{N}}$

$w\pi d$ wト n.C $\grave{m}\tau_{4}(g_{\{})$

$\mathfrak{g}_{mm^{t}S}$ in$\mu^{1}\mathfrak{h}$ $\ovalbox{\tt\small REJECT}$ $\lambda_{\phi}(\oint_{R})>,$ $k(\lambda l\beta))$

$s_{t\grave{\mathcal{M}}\omega}$ $h\alpha k_{\mathfrak{m}}$.

$\not\in$ $f$ tu $V_{1}(S_{\mathcal{D}}(R\backslash )$ 妬賦

$\varphi A\theta\backslash$ $\mathfrak{D}>\mathfrak{b}$$\mathcal{M}$ $\dot{\mathcal{M}}$ &m $a\nu$

$\Lambda\ \infty$

$4$ $\mathcal{T}_{4}\zeta\_{\mathfrak{h}})$

/ 禍\subset $\theta$

$\forall v>\mathfrak{b}$ $\chi_{\phi q_{R})}$ $>_{J}h(Q(\theta))$ .

..$ $\iota_{\alpha}\Psi^{B}$.

$\iota$

$k(t_{1t^{c_{C}}}^{1}?wS_{\triangleright}(R|S_{\Phi}\zeta R\backslash$

$\forall b\nu\iota$

$w^{S}$《 W鼠 $c$ @p $C\hslash$}

58

$E_{x}$

憂

. Ag禍 w\downarrow $\mathfrak{D}>\mathfrak{h}$ . $I\{\lambda kh^{m\omega}4\#$ $r$ $K(\iota]$

$\grave{u}M\dot{w}\wp\eta 3_{I1\uparrow}r*xdw_{\psi^{*}wA}bhm$

徽辻

59

$.\mathfrak{B}$:$\sigma uA^{\cdot}$ $4$ $h$ $,r\triangleleft 4$ 也 E-

’ $hm$ $R\vee$ A $|$rd $m’\wp*$

’ $\mathcal{D}\psi w$$\mathfrak{D}_{1}$ :

$->$\forall 唖

’

$r$ $bM$ ,. 6 $d$ a $Ma4.A$ $d$ $D\Rightarrow\theta$ !

$fu_{\Re u}\eta jbd\alpha 0W\alpha rk)\iota_{d}$

60