On equivalences of branched coverings and their action on homology
type: Item
instance of: scholarly article
title: On equivalences of branched coverings and their action on homology
zbMATH Open document ID: 0567.57002
author: William H. Kazez
published in: Pacific Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: This paper studies equivalences of stable simple branched coverings of surfaces. We give necessary and sufficient conditions for a pair of homeomorphisms f and g of surfaces M and N respectively to be homologous to homeomorphisms \(\bar f\) and \(\bar g\) which form an equivalence of two prespecified stable simple branched covers \(\psi_ 1\) and \(\psi_ 2\). That is, homeomorphisms \(\bar f\) and \(\bar g\) such that \(\psi_ 2\bar f=\bar g\psi_ 1\) are shown to exist if and only if \(\psi_{2*}f_*=g_*\psi_{1*}\) from \(H_*(M)\) to \(H_*(N).\) The proof relies on a uniqueness theorem of Hamilton and Berstein, Edmonds to restate the problem in terms of self equivalences of certain simple branched covers. Many equivalences of branched covers are constructed, and it is shown that the action on homology of these equivalences generates an appropriate subgroup of the symplectic group.
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57N05
zbMATH DE Number: 3905462
zbMATH Keywords: stable simple branched coverings of surfaces
zbMATH Keywords: action on homology
MaRDI profile type: Publication
full work available at URL: pjm.1985.118.133
OpenAlex ID: W2087308430
DOI: 10.2140/PJM.1985.118.133
description: scientific article; zbMATH DE number 3905462