Volume 11, issue 3 (2011)

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Obtaining presentations from group actions without making choices

Andrew Putman

Algebraic & Geometric Topology 11 (2011) 1737–1766
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