Canonical decompositions for Poincaré duality pairs
arXiv:math/0703890
Abstract
The authors previously described an algebraic analogue of the JSJ-decomposition of a 3-manifold. This analogue is defined for any finitely presented, one-ended group. We study this analogue in the special case of Poincaré duality pairs.
v1: 120 pages. v2: 124 pages. v3: 107 pages. New title, sections 2 and 3 removed, as the theory therein has been developed more thoroughly and generally by the authors and Vincent Guirardel. v4: 126 pages, no figures. Added a new section showing that under doubling of a Poincaré duality pair, our decomposition behaves like the JSJ-decomposition of a 3-manifold