Obtaining presentations from group actions without making choices

Details Obtaining presentations from group actions without making choices Obtaining presentations from group actions without making choices

2009-01-26

arxiv.org/abs/0901.4089v3

Mathematics

Group Theory

24 pages, 8 figures. Some small corrections. To appear in Algebr. Geom. Topol

Scientific paper

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.

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