On One Application of Asphericity of Presentations

2025/04/28 by Maxim Zykin, Zykin, Maxim
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2504.20210

openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I present a direct proof of Lemma 3(a) from O. V. Kulikova's work on torsion in the group F/[M,N], using only Proposition 1.2 of Chiswell-Collins-Huebschmann on combinatorially aspherical presentations. In particular, I show that if two presentations satisfy the RC condition and are combinatorially aspherical, then the quotient N/[F,N] is free abelian on the defining relators and central in F/[F,N], whence the extension F/[M,N] is torsion-free.

Citations

• Aspherical group presentations

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