Coarse Alexander duality and duality groups
Abstract
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 (n1) 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 ndimensional Poincare duality pair. In particular, if G is a 2dimensional 1ended 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 1999
 DOI:
 10.48550/arXiv.math/9911003
 arXiv:
 arXiv:math/9911003
 Bibcode:
 1999math.....11003K
 Keywords:

 Geometric Topology;
 Group Theory;
 57P10;
 57M60;
 20F32;
 20J05
 EPrint:
 47 pages