Obtaining presentations from group actions without making choices

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.

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

References in corpus (1)

• An infinite presentation of the Torelli group

Cited by in corpus (5)

• Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at t=-1
• A generating set for the palindromic Torelli group
• On the second homology group of the Torelli subgroup of Aut(F_n)
• Equivariant group presentations and the second homology group of the Torelli group
• Cutting and Pasting in the Torelli subgroup of Out($F_n$)