Measuring the size of the coincidence set
type: Item
instance of: scholarly article
title: Measuring the size of the coincidence set
zbMATH Open document ID: 1031.55001
DOI: 10.1016/S0166-8641(01)00292-9
author: Jan Jaworowski
author: Pedro L. Q. Pergher
author: Daciberg Lima Gonçalves
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: Let \(G\) be a finite group which acts freely on an \(m\)-sphere \(S^m\). Let \(H\) be a subgroup of \(G\), then \(H\) acts on each \(G\)-orbit \(Gx\) by: \(h(gx)= (gh)x\) for all \(g\in G\). For a map \(f: S^m\to Y\) to a \(k\)-dimensional CW-complex, call \(x\in S^m\) an \((H,G)\)-coincidence point of \(f\) if \(f\) sends every orbit of the action of \(H\) on \(Gx\) to a single point. The set of \((H,G)\)-coincidence points is denoted by \(A(f,H,G)\). In a previous paper, the authors proved that if \(m\geq|G|k\), then there is a nontrivial subgroup \(H\) of \(G\) such that \(A(f,H,G)\) is nonempty. In the present paper, they prove that if \(H\) is a normal subgroup of \(G\) that is cyclic of prime order, then the covering dimension of \(A(f,H,G)\) is at least \(m-|G|k\).
reviewed by: Robert F. Brown
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 55M10
Mathematics Subject Classification ID: 55M35
zbMATH DE Number: 1879137
zbMATH Keywords: \(G\)-coincidence
zbMATH Keywords: equivariant
zbMATH Keywords: \(G\)-index
zbMATH Keywords: \(G\)-action
zbMATH Keywords: \((H,G)\)-coincidence
zbMATH Keywords: transfer
zbMATH Keywords: Smith sequence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1879137