on well- definedness o f local index topology of torus actions and

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On well-definedness of local index Topology of torus actions and its applications to geometry and combinatorics Hajime Fujita Japan women’s university

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On well- definedness o f local index Topology of torus actions and its applications to geometry and combinatorics. Hajime Fujita Japan women’s university. Joint work with M. Furuta & T. Yoshida. 1/18. Main subject of this talk. 2/18. Contents. §1. Compatible fibration. - PowerPoint PPT Presentation

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Page 1: On well- definedness o f local index Topology of torus actions and

On well-definedness of local index

Topology of torus actions and its applications to geometry and

combinatorics

Hajime FujitaJapan women’s university

Page 2: On well- definedness o f local index Topology of torus actions and

Joint work with M. Furuta & T. Yoshida

1/18

Page 3: On well- definedness o f local index Topology of torus actions and

Main subject of this talk

2/18

Page 4: On well- definedness o f local index Topology of torus actions and

§1. Compatible fibration

§2. Compatible system

§3. Local index

§4. Well-definedness of local index

Contents

3/18

Page 5: On well- definedness o f local index Topology of torus actions and

§1. Compatible fibration

4/18

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5/18

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6/18

Page 8: On well- definedness o f local index Topology of torus actions and

7/18

Page 9: On well- definedness o f local index Topology of torus actions and

§2. Compatible system

8/18

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9/18

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10/18

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11/18

Page 13: On well- definedness o f local index Topology of torus actions and

12/18

Page 14: On well- definedness o f local index Topology of torus actions and

§3. Local index

13/18

Page 15: On well- definedness o f local index Topology of torus actions and

14/18

Page 16: On well- definedness o f local index Topology of torus actions and

§4. Well-definedness of local index

15/18

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16/18

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17/18

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18/18

Page 20: On well- definedness o f local index Topology of torus actions and

Thank you for your attention!!

Page 21: On well- definedness o f local index Topology of torus actions and

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

Page 22: On well- definedness o f local index Topology of torus actions and

Proof of the cobordism invariance

Page 23: On well- definedness o f local index Topology of torus actions and

Proof of the cobordism invariance

Page 24: On well- definedness o f local index Topology of torus actions and

Proof of the cobordism invariance

Page 25: On well- definedness o f local index Topology of torus actions and

Proof of the cobordism invariance

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