Equivariant Nielsen fixed point theory for G-maps
type: Item
instance of: scholarly article
title: Equivariant Nielsen fixed point theory for G-maps
zbMATH Open document ID: 0691.55004
author: Jianyong Qiao
author: Sumit K. Garg
published in: Pacific Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Let f: \(V\to X\) be a G-map defined on an open invariant subset V of a G- ENR X where G is a compact Lie group and the G-action on V is not necessarily free. In this paper, we introduce the notion of an equivariant Nielsen number \(N^ c_ G(f,V)\) which is an ordered k-tuple that depends on the isotropy types \((H_ 1),...,(H_ k)\) of V. When G is finite, \(N^ c_ G(f,V)\) gives a lower bound for the minimal number of fixed points in the (restricted) G-homotopy class of f and this lower bound is sharp when the G-action of V is free. We relate \(N^ c_ G(f,V)\) to a local equivariant obstruction to G-deforming a map to be fixed point free and we discuss the relationship between the equivariant Nielsen number and the ordinary Nielsen number.
Mathematics Subject Classification ID: 55M20
zbMATH DE Number: 4131257
zbMATH Keywords: G-action
zbMATH Keywords: equivariant Nielsen number
zbMATH Keywords: fixed points
zbMATH Keywords: ordinary Nielsen number
MaRDI profile type: Publication
full work available at URL: pjm.1991.150.179
OpenAlex ID: W1977374932
DOI: 10.2140/PJM.1991.150.179
description: scientific article; zbMATH DE number 4131257