The index of transversally elliptic operators for locally free actions
type: Item
instance of: scholarly article
title: The index of transversally elliptic operators for locally free actions
zbMATH Open document ID: 0793.19003
author: Jeffrey Fox
author: Peter Haskell
published in: Pacific Journal of Mathematics
publication date: 1994-08-18T00:00:00Z
review text: Let a connected unimodular Lie group \(G\) act smoothly and locally freely on a closed manifold \(X\). Assume that the isotropy groups of the action are torsion-free. Let \(K\) be the maximal compact subgroup of \(G\). Let \(T\) be a \(G\)-invariant first order differential operator on \(X\) that is ellipitic in directions transverse to the \(G\)-orbits. Using Kasparov products over \(C^* G\), the paper proves index formulas equating indices of elliptic operators on \(K\setminus X\) with linear combinations of multiplicities of \(G\)-representations in \(\text{kernel}(T)- \text{kernel}(T^*)\).
reviewed by: Peter Haskell
Mathematics Subject Classification ID: 19K56
Mathematics Subject Classification ID: 58J20
zbMATH DE Number: 589809
zbMATH Keywords: transversally elliptic operators
zbMATH Keywords: locally free actions
zbMATH Keywords: index-theoretic multiplicity of representations
zbMATH Keywords: Kasparov products
zbMATH Keywords: index formulas
MaRDI profile type: Publication
full work available at URL: pjm.1994.164.41
OpenAlex ID: W1970661025
DOI: 10.2140/PJM.1994.164.41
description: scientific article; zbMATH DE number 589809