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arXiv · 1707.09799

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

P. Christopher Staecker
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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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P. Christopher Staecker. 2017-07-31. Axioms for the fixed point index of n-valued maps, and some applications. https://arxiv.org/abs/1707.09799

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