2025/05/30 by Jesús A. Álvarez López, López, Jesús A. Álvarez, Alejandro O. Majadas-Moure +3
Computer Science · #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2505.24530
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.