# Atelier de travail annuel du projet SINGSTAR 2017

6-9 November 2017
Saint Flour
Europe/Paris timezone

## Smooth $K$-theory

8 Nov 2017, 09:00
50m
Hôtel des Planchettes (Saint Flour)

### Hôtel des Planchettes

#### Saint Flour

7 Rue des Planchettes, 15100 Saint-Flour

Alain Berthomieu

### Description

Smooth K-theory is defined on a smooth manifold as an extension of topological K-theory by differential forms. In the case of a proper submersion, direct image for smooth K-theory is defines using Bismut and al.'s eta-forms, which are differential forms entering in the transgression of the local families index theorem. The construction of a direct image in the case of a closed immersion should use corresponding objects which are currents instead of smooth differential forms.

### Presentation Materials

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