Algebraic & Geometric Topology

Torsion homology and cellular approximation

Ramón Flores and Fernando Muro

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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.

Article information

Algebr. Geom. Topol., Volume 19, Number 1 (2019), 457-476.

Received: 27 March 2018
Revised: 3 September 2018
Accepted: 11 September 2018
First available in Project Euclid: 12 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F99: None of the above, but in this section 55P60: Localization and completion

Torsion homology cellular group


Flores, Ramón; Muro, Fernando. Torsion homology and cellular approximation. Algebr. Geom. Topol. 19 (2019), no. 1, 457--476. doi:10.2140/agt.2019.19.457.

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