We describe the role of the Schur multiplier in the structure of the –torsion of discrete groups. More concretely, we show how the knowledge of allows us to approximate many groups by colimits of copies of –groups. Our examples include interesting families of noncommutative infinite groups, including Burnside groups, certain solvable groups and branch groups. We also provide a counterexample for a conjecture of Emmanuel Farjoun.
"Torsion homology and cellular approximation." Algebr. Geom. Topol. 19 (1) 457 - 476, 2019. https://doi.org/10.2140/agt.2019.19.457