Homology, Homotopy and Applications

Volume 19 (2017)

Number 2

On the dimension of classifying spaces for families of abelian subgroups

Pages: 83 – 87

DOI: https://dx.doi.org/10.4310/HHA.2017.v19.n2.a5

Authors

Ged Corob Cook (Department of Mathematics, University of Southampton, United Kingdom)

Victor Moreno (Department of Mathematics, Royal Holloway, University of London, Egham, United Kingdom)

Brita Nucinkis (Department of Mathematics, Royal Holloway, University of London, Egham, United Kingdom)

Federico W. Pasini (Department of Mathematics, University of Western Ontario, London, On., Canada)

Abstract

We show that a finitely generated abelian group $G$ of torsion-free rank $n \geqslant 1$ admits an $(n+r)$-dimensional model for $E_{\mathfrak{F}_r} G$, where $\mathfrak{F}_r$ is the family of subgroups of torsion-free rank less than or equal to $r \geqslant 0$.

Keywords

classifying space for a family, abelian group

2010 Mathematics Subject Classification

18G99, 20J06, 55R35

Full Text (PDF format)

The first author was partially supported by EPSRC grant EP/N007328/1 and the fourth author gratefully acknowledges the support by the Italian National Group for Algebraic and Geometric Structures and Their Applications (GNSAGA – INDAM).

Received 29 September 2016

Published 6 September 2017