Local formulae in equivariant bordisms
type: Item
instance of: scholarly article
title: Local formulae in equivariant bordisms
zbMATH Open document ID: 0777.57014
DOI: 10.1016/0040-9383(92)90004-2
author: Gabriel Katz
published in: Topology
publication date: 1993-05-16T00:00:00Z
review text: It is well known that if one localizes an equivariant bordism group \(\Omega^ G_ *(X)\) at certain primes dividing the order of \(G\), the result is a direct sum of ordinary bordism groups for the fixed sets of subgroups and appropriate normal bundles. In earlier work, the author established a formalism for this decomposition in terms of characteristic classes in cobordism theory. This paper is devoted to establishing the universal local formula for the fixed set of \(G\) itself. The main result is a formula for the equivariant Witt invariant, analogous to the Atiyah-Singer \(G\)-signature theorem.
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 55N22
zbMATH DE Number: 167779
zbMATH Keywords: equivariant bordism group
zbMATH Keywords: fixed sets
zbMATH Keywords: characteristic classes
zbMATH Keywords: Atiyah- Singer \(G\)-signature theorem
MaRDI profile type: Publication
full work available at URL: 0040-9383(92)90004-2
OpenAlex ID: W2009708445
description: scientific article; zbMATH DE number 167779