Volume 14, issue 5 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Lifting group actions, equivariant towers and subgroups of non-positively curved groups

Richard Gaelan Hanlon and Eduardo Martínez-Pedroza

Algebraic & Geometric Topology 14 (2014) 2783–2808
Abstract

If C is a class of complexes closed under taking full subcomplexes and covers and G is the class of groups admitting proper and cocompact actions on one-connected complexes in C, then G is closed under taking finitely presented subgroups. As a consequence the following classes of groups are closed under taking finitely presented subgroups: groups acting geometrically on regular CAT(0) simplicial complexes of dimension 3, k–systolic groups for k 6, and groups acting geometrically on 2–dimensional negatively curved complexes. We also show that there is a finite non-positively curved cubical 3–complex that is not homotopy equivalent to a finite non-positively curved regular simplicial 3–complex. We include applications to relatively hyperbolic groups and diagrammatically reducible groups. The main result is obtained by developing a notion of equivariant towers, which is of independent interest.

Keywords
non-positively curved groups, hyperbolic groups, $\mathrm{CAT}(0)$, diagrammatically reducible, systolic, relatively hyperbolic, towers, van Kampen diagrams, equivariant covers, equivariant towers
Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 57M07
References
Publication
Received: 9 July 2013
Revised: 5 March 2014
Accepted: 15 March 2014
Published: 6 November 2014
Authors
Richard Gaelan Hanlon
Department of Mathematics and Statistics
Memorial University of Newfoundland
St. John’s NL A1C 5S7
Canada
Eduardo Martínez-Pedroza
Department of Mathematics and Statistics
Memorial University of Newfoundland
St. John’s NL A1C 5S7
Canada
http://www.math.mun.ca/~emartinezped/