Obtaining presentations from group actions without making choices

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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.

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APA

Putman, A. (2011). Obtaining presentations from group actions without making choices. Algebraic and Geometric Topology, 11(3), 1737–1766. https://doi.org/10.2140/agt.2011.11.1737

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