On the LS-category of homomorphisms of groups with torsion

2023/02/21 by Nursultan Kuanyshov, Kuanyshov, Nursultan · 2 citations
Mathematics · #20K10 #20K30 #20K45 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 55M30 #Secondary 20J06

paper · pdf · doi:10.48550/arxiv.2302.10998

openalex publication_date 2023/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the equality \cat(ϕ)=\cd(ϕ) for homomorphisms ϕ:Γ→ Λ between finitely generated abelian groups Γ and Λ, where ϕ(T(Γ))=0 for the torsion subgroups T(Γ) of Γ.

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• Cohomological dimension of a Lie algebra homomorphism
• Small Value of cohomological dimension of group homomorphisms

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