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A Reidemeister trace for fibred maps. (English) Zbl 1232.55005

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 {Top} and the notion of cellular cell complex for an \(\mathcal{F}\)-complex as defined by 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

MSC:

55M20 Fixed points and coincidences in algebraic topology
55R65 Generalizations of fiber spaces and bundles in algebraic topology
55R70 Fibrewise topology

Citations:

Zbl 1053.55014
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References:

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