Computing the one-parameter Nielsen number for homotopies on the n-torus

2021/03/24 by Weslem Liberato Silva, Silva, Weslem Liberato
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2103.13529

openalex publication_date 2021/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F: Tⁿ × I → Tⁿ be a homotopy on a n-dimensional torus. The main purpose of this paper is to present a formula for the one-parameter Nielsen number N(F) of F in terms of its induced homomorphism. If L(F) is the one-parameter Lefschetz class of F then L(F) is given by L(F) = N(F)α, for some α∈ H₁(π₁(Tⁿ),ℤ).

Related

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