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

2017/07/31 by P. Christopher Staecker, Staecker, P. Christopher · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Peroxisome Proliferator-Activated Receptors #math.AT #math.GN

paper · pdf · doi:10.48550/arxiv.1707.09799

arxiv created 2017/07/31 · openalex publication_date 2017/07/31 · arxiv updated 2017/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 invariance, additivity, and a splitting property. This uniqueness is used to obtain easy proofs of an averaging formula and product formula for the index. In the setting of n-valued maps on a manifold, we show that the axioms can be weakened.

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• Nielsen coincidence theory of (n,m)-valued pairs of maps

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