On the LS-category of homomorphism of almost nilpotent groups

Abstract

We prove the equality $\cat(ϕ)=\cd(ϕ)$ for epimorphisms $\varphi :\Gamma \to \Lambda$ between torsion-free, finitely generated almost nilpotent groups $\Gamma$ and $\Lambda$. In addition, we prove the equality $\cat(ϕ)=\cd(ϕ)$ for homomorphisms $\varphi :\Gamma \to \Lambda$ between torsion-free, finitely generated virtually nilpotent groups.

9 pages