A Reidemeister trace for fibred maps
type: Item
instance of: scholarly article
title: A Reidemeister trace for fibred maps
zbMATH Open document ID: 1232.55005
author: Davide L. Ferrario
published in: Journal of Fixed Point Theory and Applications
publication date: 2011-11-04T00:00:00Z
review text: This is a rather complicated and demanding article describing how to define a Reidemeister trace in the context of fibred CW-complexes and fibred maps. The basic difficulty consists in finding a substitute for the universal covering in the fibred situation. The main tool is the concept of \(\mathcal{F}\)-family for a small category \(\mathcal{F}\) which is faithfully embedded in {\textbf{Top}} and the notion of cellular cell complex for an \(\mathcal{F}\)-complex as defined by \textit{H.-J. Baues} and the author [Topology Appl. 139, No. 1--3, 63--96 (2004; Zbl 1053.55014)]. Then it is relatively easy to define a trace and the Reidemeister trace of a cellular \(\mathcal{F}\)-map as an alternating sum of diagonal terms of the induced chain morphisms
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 55R65
Mathematics Subject Classification ID: 55R70
zbMATH DE Number: 5968117
zbMATH Keywords: Reidemeister trace
zbMATH Keywords: fibred map
zbMATH Keywords: fibred CW-complex
reviewed by: Christian Fenske
MaRDI profile type: Publication
full work available at URL: s11784-011-0051-2
OpenAlex ID: W2064984885
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DOI: 10.1007/S11784-011-0051-2
description: scientific article; zbMATH DE number 5968117