A comparison principle and extension of equivariant maps
type: Item
instance of: scholarly article
title: A comparison principle and extension of equivariant maps
zbMATH Open document ID: 0829.55002
DOI: 10.1007/BF02567612
author: A. Kushkuley
author: Zalman Balanov
published in: Manuscripta Mathematica
publication date: 1996-01-15T00:00:00Z
full work available at URL: https://eudml.org/doc/155959
review text: This work unifies and extends many generalizations of Borsuk's theorem. The authors prove an equivariant version of the Kuratowski-Dugundji Theorem. In order to do this, they show the existence of a (quasi)- fundamental domain for any free action of a compact Lie group on a metric space \(X\). Then for \(G\) finite and \(\Psi, \varphi : M \to S\) a pair of equivariant maps where \(M\) is a manifold of the same dimension \(n\) as the sphere \(S\), they show that \(\deg \Psi - \deg \varphi \equiv 0 \pmod {\text{GCD} \{|G/H_i |\}}\) under certain hypotheses. Finally they show that \(n - k\) is a lower bound for the genus of \(S\smallsetminus B\) where \(S\smallsetminus B\) is a free \(G\)-subspace and \(B\) the image of a smooth mapping of a \(k\)-dimensional compact manifold.
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 55M35
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 57S15
zbMATH DE Number: 624934
zbMATH Keywords: fundamental domain
zbMATH Keywords: free action of a compact Lie group on a metric space
zbMATH Keywords: equivariant maps
reviewed by: Daciberg Lima Gonçalves
MaRDI profile type: Publication
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OpenAlex ID: W2047584509
description: scientific article; zbMATH DE number 624934