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A Lefschetz type homomorphism for coincidence of several maps
Abstract
Given p-maps f1, ⋯, fp : X → M, p ≥ 2, from an arbitrary topological space to an orientable closed connected m-manifold, in this paper we define a graded homomorphism Λf1 ⋯ fp: H(X) → H(Mp−1) of degree −m(p−1) called by Lefschetz homomorphism. If the Lefschetz homomorphism is nontrivial then there is a point x ∈ X such that f1(x) = ⋯ = fp(x). The Lefschetz homomorphism Λf1 ⋯ fp can be represented as a Knill-like trace.
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BibTeX
@misc{silva2026lefschetz,
title = {{A Lefschetz type homomorphism for coincidence of several maps}},
author = {Pryscilla dos Santos Ferreira Silva and Weslem Liberato Silva},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.12183},
eprint = {2607.12183},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.12183},
}
RIS
TY - UNPB
TI - A Lefschetz type homomorphism for coincidence of several maps
AU - Pryscilla dos Santos Ferreira Silva
AU - Weslem Liberato Silva
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2607.12183
UR - https://arxiv.org/abs/2607.12183
AB - Given p-maps f_1, ⋯, f_p : X → M, p ≥ 2, from an arbitrary topological space to an orientable closed connected m-manifold, in this paper we define a graded homomorphism Λ_f_1 ⋯ f_p: H(X) → 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 ∈ X such that f_1(x) = ⋯ = f_p(x). The Lefschetz homomorphism Λ_f_1 ⋯ f_p can be represented as a Knill-like trace.
ER -