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Feb 2005 Coarse Alexander duality and duality groups
Michael Kapovich, Bruce Kleiner
J. Differential Geom. 69(2): 279-352 (Feb 2005). DOI: 10.4310/jdg/1121449108

Abstract

We study discrete group actions on coarse Poincaré duality spaces, e.g., acyclic simplicial complexes which admit free cocompact group actions by Poincaré duality groups. When G is an (n−1) dimensional duality group and X is a coarse Poincaré duality space of formal dimension n, then a free simplicial action GX determines a collection of “peripheral” subgroups H1, … HkG so that the group pair (G, {H1,…Hk }) is an n-dimensional Poincaré duality pair. In particular, if G is a 2-dimensional 1-ended group of type FP2, and GX is a free simplicial action on a coarse PD(3) space X, 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. In the process, we develop coarse topological language and a formulation of coarse Alexander duality which is suitable for applications involving quasi-isometries and geometric group theory.

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Michael Kapovich. Bruce Kleiner. "Coarse Alexander duality and duality groups." J. Differential Geom. 69 (2) 279 - 352, Feb 2005. https://doi.org/10.4310/jdg/1121449108

Information

Published: Feb 2005
First available in Project Euclid: 15 July 2005

zbMATH: 1086.57019
MathSciNet: MR2168506
Digital Object Identifier: 10.4310/jdg/1121449108

Rights: Copyright © 2005 Lehigh University

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Vol.69 • No. 2 • Feb 2005
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