Transfers for ramified covering maps in homology and cohomology
type: Item
instance of: scholarly article
title: Transfers for ramified covering maps in homology and cohomology
zbMATH Open document ID: 1117.55012
DOI: 10.1155/IJMMS/2006/94651
author: Marcelo Aguilar
author: Carlos Prieto
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2007-06-14T00:00:00Z
full work available at URL: https://eudml.org/doc/53291
review text: This paper provides a neat topological description of a homology transfer for ramified covering maps. The construction is based on the identification of the reduced singular homology group \(\tilde{H}_q(X;L)\) (for any abelian group \(L\)) with the homotopy group \(\pi_q(F(X,L))\) of the abelian group \(F(X,L)\) of all functions \(X \to L\) having finite support and mapping the base-point of \(X\) to the zero element of \(L\). Given a ramified covering map \(E \to X\), a natural construction is given of a pre-transfer \(F(X,L) \to F(E,L)\) which, in turn, induces the homology transfer. As this approach to homology groups has been used in other contexts (e.g. non-commutative geometry and algebraic geometry), this approach to the transfer can be translated very directly into those contexts. This enables the authors to give slicker proofs of some established results and also to prove some new theorems.
reviewed by: Martin D. Crossley
Mathematics Subject Classification ID: 55R12
Mathematics Subject Classification ID: 55R65
zbMATH DE Number: 5164297
zbMATH Keywords: Transfer
zbMATH Keywords: ramified covering
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5164297