On the LS-category of homomorphisms of groups with torsion

TL;DR

This paper establishes an equality between the LS-category and cohomological dimension for certain homomorphisms between finitely generated abelian groups, specifically those annihilating torsion subgroups.

Contribution

It proves the equality () for homomorphisms between finitely generated abelian groups that send torsion to zero, clarifying their algebraic topological properties.

Findings

() equals () for these homomorphisms

The result applies to homomorphisms with torsion subgroup kernel

Provides new insights into the algebraic topology of abelian group homomorphisms

Abstract

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