Equivariant vector fields and self-maps of spheres.
type: Item
instance of: scholarly article
title: Equivariant vector fields and self-maps of spheres.
zbMATH Open document ID: 1046.57019
author: S. R. Costenoble
author: S. Waner
published in: Journal of Pure and Applied Algebra
publication date: 2004-02-02T00:00:00Z
review text: This is a new tentative to generalize the Euler characteristic definition in the equivariant situation. The purpose here is to recover the property to be the unique obstruction to the existence of a nowhere zero smooth equivariant tangent vector field by a compact Lie group action. The authors introduce first pseudotransversality results for equivariant vector fields, then they define the strong equivariant Euler characteristic of a G-CW complex as the equivariant transfer associated to the fibration \(X \mapsto *\). As a corollary they give the calculus of the monoid of self-maps of a sphere.
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 18B40
Mathematics Subject Classification ID: 57R91
Mathematics Subject Classification ID: 55P91
zbMATH DE Number: 2035895
zbMATH Keywords: Euler characteristic
zbMATH Keywords: equivariant vector fields
reviewed by: Raymond Barre
MaRDI profile type: Publication
full work available at URL: j.jpaa.2003.07.009
OpenAlex ID: W2126935250
cites work: The equivariant Euler characteristic
cites work: The equivariant triangulation theorem for actions of compact Lie groups
cites work: Equivariant stable homotopy theory. With contributions by J. E. McClure
cites work: The local structure of tangent G-vector fields
cites work: Equivariant SKK and vector field bordism
DOI: 10.1016/J.JPAA.2003.07.009
description: scientific article; zbMATH DE number 2035895