On well-definedness of local index

Topology of torus actions and its applications to geometry and

combinatorics

Hajime FujitaJapan women’s university

Joint work with M. Furuta & T. Yoshida

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Main subject of this talk

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§1. Compatible fibration

§2. Compatible system

§3. Local index

§4. Well-definedness of local index

Contents

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§1. Compatible fibration

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§2. Compatible system

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§3. Local index

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§4. Well-definedness of local index

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Thank you for your attention!!

Proof of the cobordism invariance

Analytic realization of transverse index by perturbation of Dirac-type operator by Clifford action of the Kirwan vector field.

Modification of the Braverman’s proof of the cobordism invariance of

the transverse index

Proof of the cobordism invariance

Proof of the cobordism invariance

Proof of the cobordism invariance

Proof of the cobordism invariance