A Combinatorial Study of the Fixed Point Index
Algebraic Topology
2025-06-02 v1
Abstract
We introduce a theory of integration with respect to the fixed point index, offering a substantial improvement over previous approaches based on the Lefschetz number. This framework eliminates several restrictive assumptions -- such as the need for definability, openness, or f-invariance of subspaces -- thereby allowing broader applicability. We also present a natural combinatorial adaptation of the fixed point index that extends the combinatorial Lefschetz number. This extension yields new topological and homotopical invariance results and facilitates the integration of real-valued functions with respect to fixed points.
Cite
@article{arxiv.2505.24530,
title = {A Combinatorial Study of the Fixed Point Index},
author = {Jesús A. Álvarez López and Alejandro O. Majadas-Moure and David Mosquera-Lois},
journal= {arXiv preprint arXiv:2505.24530},
year = {2025}
}