Axioms for the fixed point index of n-valued maps, and some applications
Algebraic Topology
2017-08-01 v1 General Topology
Abstract
We give an axiomatic characterization of the fixed point index of an -valued map. For -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 -valued maps on a manifold, we show that the axioms can be weakened.
Keywords
Cite
@article{arxiv.1707.09799,
title = {Axioms for the fixed point index of n-valued maps, and some applications},
author = {P. Christopher Staecker},
journal= {arXiv preprint arXiv:1707.09799},
year = {2017}
}