A formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles
P. Christopher Staecker
TL;DR
This paper presents a formula for calculating the coincidence Reidemeister trace of selfmaps on bouquets of circles using Fox calculus, linking it to the problem of identifying doubly twisted conjugacy classes in free groups.
Contribution
It introduces a novel formula that simplifies the computation of the coincidence Reidemeister trace for selfmaps on bouquets of circles, connecting it to free group conjugacy classes.
Findings
Provides a Fox calculus-based formula for the Reidemeister trace
Reduces the problem to distinguishing doubly twisted conjugacy classes
Facilitates computation of coincidence invariants in topological maps
Abstract
We give a formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles in terms of the Fox calculus. Our formula reduces the problem of computing the coincidence Reidemeister trace to the problem of distinguishing doubly twisted conjugacy classes in free groups.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry