On the LS-category of homomorphisms

Alexander Dranishnikov, Nursultan Kuanyshov

We prove the equality $\cat(ϕ)=\cd(ϕ)$ for homomorphisms $\varphi :\Gamma \to \Lambda$ of a torsion free finitely generated nilpotent groups $\Gamma$ to an arbitrary group $\Lambda$. We construct an epimorphism…