A Lefschetz type homomorphism for coincidence of several maps

Pryscilla dos Santos Ferreira Silva; Weslem Liberato Silva

A Lefschetz type homomorphism for coincidence of several maps

Algebraic Topology 2026-07-13 v1

Authors: Pryscilla dos Santos Ferreira Silva , Weslem Liberato Silva

Abstract

Given $p$ -maps $f_1, \cdots, f_p : X \to M,$ $p \geq 2,$ from an arbitrary topological space to an orientable closed connected $m$ -manifold, in this paper we define a graded homomorphism $\Lambda_{f_1 \cdots f_p}: H(X) \to H(M^{p-1})$ of degree $-m(p-1)$ called by Lefschetz homomorphism. If the Lefschetz homomorphism is nontrivial then there is a point $x \in X$ such that $f_1(x) = \cdots = f_p(x).$ The Lefschetz homomorphism $\Lambda_{f_1 \cdots f_p}$ can be represented as a Knill-like trace.

Keywords

Lefschetz homomorphism coincidence theory multiple maps graded homomorphism Knill trace orientable manifold

Cite

@article{arxiv.2607.12183,
  title  = {A Lefschetz type homomorphism for coincidence of several maps},
  author = {Pryscilla dos Santos Ferreira Silva and Weslem Liberato Silva},
  journal= {arXiv preprint arXiv:2607.12183},
  year   = {2026}
}