Abstract
A geometric hypothesis is presented under which the cohomology of a groupGgiven by generators and defining relators can be computed in terms of a groupHdefined by a subpresentation. In the presence of this hypothesis, which is framed in terms of spherical pictures, one has thatHis naturally embedded inG, and that the finite subgroups ofGare determined by those ofH. Practical criteria for the hypothesis to hold are given. The theory is applied to give simple proofs of results of Collins-Perraud and of Kanevskiĭ. In addition, we consider in detail the situation whereGis obtained fromHby adjoining a single new generatorxand a single defining relator of the formxaxbxεc, wherea, b, c ∈ Hand |ε| = 1.
Publisher
Cambridge University Press (CUP)
Cited by
68 articles.
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