Homological data on the periodic structure of self-maps on wedge sums

TL;DR

This paper investigates the periodic points of continuous self-maps on wedge sums of manifolds, focusing on algebraic invariants like Lefschetz numbers and obstructions, especially for wedge sums of tori.

Contribution

It provides explicit computations of algebraic invariants and analyzes homological obstructions for self-maps on wedge sums of manifolds, including tori.

Findings

Explicit formulas for Lefschetz numbers and Dold coefficients.

Identification of homological obstructions in defining self-maps.

Analysis of algebraic periods for maps on wedge sums.

Abstract

In this article, we study the periodic points for continuous self-maps on the wedge sum of topological manifolds, exhibiting a particular combinatorial structure. We compute explicitly the Lefschetz numbers, the Dold coefficients and consider its set of algebraic periods. Moreover, we study the special case of maps on the wedge sum of tori, and show some of the homological obstructions present in defining these maps.