Coarse Alexander duality and duality groups

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We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n-1) dimensional duality group and X is a coarse Poincare duality space of formal dimension n, then a free simplicial action of G on X determines a collection of ``peripheral'' subgroups F_1,...,F_k in G so that the group pair (G;F_1,...,F_k) is an n-dimensional Poincare duality pair. In particular, if G is a 2-dimensional 1-ended group of type FP_2, and X is a coarse PD(3) space, then G contains surface subgroups; if in addition X is simply connected, then we obtain a partial generalization of the Scott/Shalen compact core theorem to the setting of coarse PD(3) spaces.
47 pages

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Geometric Topology, Group Theory, 57P10, 57M60, 20F32, 20J05

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http://salesiana.dossiersoluciones.com/handle/123456789/79325

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9911003
 http://arxiv.org/abs/math/9911003

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arXiv