An averaging formula for Reidemeister traces

Liu, Jiyou; Zhao, Xuezhi

doi:10.12775/tmna.2015.034

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A Local Reidemeister Trace and An Averaging Formula1

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Cited by 4 publications

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“…Various limited averaging results for the Nielsen number appeared in [9], which make some specific assumptions on the maps used. Nevertheless a full averaging formula (without making these assumptions) was demonstrated for the Reidmeister trace in [11]. This averaging formula was extended to Nielsen coincidence theory in [10].…”

Section: A Local Reidemeister Trace and An Averaging Formulamentioning

confidence: 99%

The Reidemeister Trace of an $n$-valued map

Staecker¹

2021

Preprint

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In topological fixed point theory, the Reidemeister trace is an invariant associated to a selfmap of a polyhedron which combines information from the Lefschetz and Nielsen numbers. In this paper we define the Reidemeister trace in the context of n-valued selfmaps of compact polyhedra. We prove several properties of the Reidemeister trace which generalize properties from the single-valued theory, and prove an averaging formula.

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Section: A Local Reidemeister Trace and An Averaging Formulamentioning

confidence: 99%