Torsion homology and cellular approximation

Flores, Ramón; Muro, Fernando

doi:10.2140/agt.2019.19.457

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Torsion homology and cellular approximation

Ramón Flores and Fernando Muro

Algebraic & Geometric Topology 19 (2019) 457–476

DOI: 10.2140/agt.2019.19.457

Abstract

We describe the role of the Schur multiplier in the structure of the $p$ –torsion of discrete groups. More concretely, we show how the knowledge of $H_{2} G$ allows us to approximate many groups by colimits of copies of $p$ –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.

Keywords

Torsion, homology, cellular, group

Mathematical Subject Classification 2010

Primary: 20F99, 55P60

References

Publication

Received: 27 March 2018

Revised: 3 September 2018

Accepted: 11 September 2018

Published: 6 February 2019

Authors

Ramón Flores
Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid Madrid Spain

Fernando Muro
Facultad de Matemáticas Departamento de Álgebra Universidad de Sevilla Sevilla Spain

Volume 19, issue 1 (2019)