# Equivariant de Rham torsions

### Abstract

The purpose of this paper is to give an explicit local formula for the difference of two natural versions of equivariant analytic torsion in de Rham theory. This difference is the sum of the integral of a Chern-Simons current and of a new invariant, the $V$-invariant of an odd dimensional manifold equipped with an action of a compact Lie group. The $V$-invariant localizes on the critical manifolds of invariant Morse-Bott functions.

The results in this paper are shown to be compatible with results of Bunke, and also our with previous results on analytic torsion forms.

## Authors

Jean-Michel Bismut

Département de Mathématiques, Université Paris-Sud, 91405 Orsay, France

Sebastian Goette

NWF 1 Mathematik, Universität Regensburg, 93040 Regensburg, Germany