On the LS-category of homomorphisms of groups with torsion

Abstract

We prove the equality $\cat(ϕ)=\cd(ϕ)$ for homomorphisms $\varphi :\Gamma \to \Lambda$ between finitely generated abelian groups $\Gamma$ and $\Lambda$, where $\varphi (T(\Gamma ))=0$ for the torsion subgroups $T(\Gamma )$ of $\Gamma$.

8 pages