On the LS-category of homomorphism of almost nilpotent groups

2023/08/28 by Nursultan Kuanyshov, Kuanyshov, Nursultan · 2 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2308.14886

Abstract

We prove the equality \cat(ϕ)=\cd(ϕ) for epimorphisms ϕ:Γ→ Λ between torsion-free, finitely generated almost nilpotent groups Γ and Λ. In addition, we prove the equality \cat(ϕ)=\cd(ϕ) for homomorphisms ϕ:Γ→ Λ between torsion-free, finitely generated virtually nilpotent groups.

Cited by

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

Related

• On the LS-category of homomorphisms
• On the LS-category of homomorphisms of groups with torsion
• On co-Hopfian nilpotent groups
• Almost group theory
• Adapted almost invariant sets and splittings of groups