The equivariant Chern character for non-compact Lie groups
type: Item
instance of: scholarly article
title: The equivariant Chern character for non-compact Lie groups
zbMATH Open document ID: 0853.57034
author: E. Getzler
published in: Advances in Mathematics
publication date: 1995-01-11T00:00:00Z
review text: If \(G\) is a Lie group, \(EG\) its classifying bundle, and \(M\) is a differentiable manifold with a smooth left \(G\)-action, then the equivariant cohomology \(H^*_G (M)\) of \(M\) is the cohomology of a homotopy quotient \(M_G= EG\times_G M\). The author presents a new model for \(H^*_G (M)\) and obtains an explicit formula for the equivariant Chern class similar to the Chern-Weil formula for the ordinary Chern class. His Chern character specializes to that of Bott if \(G\) is discrete, and to that of Berline and Vergne if \(G\) is compact and the connection of the equivariant bundle is \(G\)-invariant.
Mathematics Subject Classification ID: 57T10
Mathematics Subject Classification ID: 55N91
zbMATH DE Number: 710356
zbMATH Keywords: Lie group
zbMATH Keywords: equivariant cohomology
zbMATH Keywords: equivariant Chern class
zbMATH Keywords: Chern-Weil formula
reviewed by: C. S. Hoo
MaRDI profile type: Publication
OpenAlex ID: W1981365291
Wikidata QID: Q115396420
DOI: 10.1006/AIMA.1994.1081
description: scientific article; zbMATH DE number 710356