Obtaining presentations from group actions without making choices

Putman, Andrew

doi:10.2140/agt.2011.11.1737

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Obtaining presentations from group actions without making choices

Andrew Putman

Algebraic & Geometric Topology 11 (2011) 1737–1766

DOI: 10.2140/agt.2011.11.1737

Abstract

Consider a group $G$ acting nicely on a simply-connected simplicial complex $X$ . Numerous classical methods exist for using this group action to produce a presentation for $G$ . For the case that $X ∕ G$ is $2$ –connected, we give a new method that has the novelty that one does not have to identify a fundamental domain for the action. Indeed, the resulting presentation is canonical in the sense that no arbitrary choices need to be made. It can be viewed as a nonabelian analogue of a simple result in the study of equivariant homology.

Keywords

group presentations, group actions

Mathematical Subject Classification 2010

Primary: 20F05, 57M07

References

Publication

Received: 6 January 2011

Accepted: 7 April 2011

Published: 3 June 2011

Authors

Andrew Putman
Department of Mathematics Rice University 6100 Main St. Houston TX 77005 USA
http://www.math.rice.edu/~andyp/

Volume 11, issue 3 (2011)