# Colloque 2013 du GDR 2875, Topologie Algébrique et Applications

16-18 October 2013
Université d'Angers
Europe/Paris timezone

## Equivariant Lefschetz formulas for smooth actions of compact groups

16 Oct 2013, 12:00
45m
Amphi L005 (bâtiment L) (Université d'Angers)

### Amphi L005 (bâtiment L)

#### Université d'Angers

Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers cedex 01
Exposé de recherche sur invitation Topologie algébrique et applications

### Speaker

Dr Ivo Dell'Ambrogio (Lille)

### Description

The classical Lefschetz-Hopf fixed-point formula equates two different computations for the trace of a self-map of a smooth compact manifold: one side computes it locally and geometrically, the other side globally and homologically. In a series of papers, Heath Emerson and Ralf Meyer generalize the geometric side to equivariant self-maps -- or even self-correspondences -- of a compact manifold acted upon by a compact Lie group. This invariant lives in the representation ring of the group. In joint work, we compute it homologically by way of topological equivariant K-theory. In particular, the formula simplifies to rather pleasing forms for finite groups and Hodgkin Lie groups. The constructions and proofs use equivariant Kasparov theory in an essential way.
Mots Clés / Keywords Lefschetz-Hopf fixed-point formula; equivariant Kasparov theory

### Presentation Materials

 Transparents