On the LS-category of homomorphism of almost nilpotent groups

Abstract

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