# Axioms for a local Reidemeister trace in fixed point and coincidence theory on differentiable manifolds

@article{Staecker2007AxiomsFA, title={Axioms for a local Reidemeister trace in fixed point and coincidence theory on differentiable manifolds}, author={P. Christopher Staecker}, journal={Journal of Fixed Point Theory and Applications}, year={2007}, volume={5}, pages={237-247} }

Abstract.We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local Reidemeister trace in coincidence theory.

#### 7 Citations

The Reidemeister Trace of an $n$-valued map

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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… Expand

Axioms for the fixed point index of n-valued maps, and some applications

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We give an axiomatic characterization of the fixed point index of an n-valued map. For n-valued maps on a polyhedron, the fixed point index is shown to be unique with respect to axioms of homotopy… Expand

An averaging formula for the coincidence Reidemeister trace

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In the setting of continuous maps between compact orientable manifolds of the same dimension, there is a well known averaging formula for the coincidence Lefschetz number in terms of the Lefschetz… Expand

A formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles

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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… Expand

The homotopy coincidence index

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- 2010

In a survey based on recent work of Koschorke, Klein and Williams, stable homotopy coincidence invariants are constructed using fibrewise methods generalizing the standard construction of the stable… Expand

Axioms for the coincidence index of maps between manifolds of the same dimension

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Abstract We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps… Expand

Axioms for the Lefschetz number as a lattice valuation

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We give new axioms for the Lefschetz number based on Hadwiger's characterization of the Euler characteristic as the unique lattice valuation on polyhedra which takes value 1 on simplices. In the… Expand

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