English

Canonical decompositions for Poincar\'e duality pairs

Group Theory 2020-04-14 v4 Geometric Topology

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 Poincar\'e duality pairs.

Cite

@article{arxiv.math/0703890,
  title  = {Canonical decompositions for Poincar\'e duality pairs},
  author = {Peter Scott and Gadde A. Swarup},
  journal= {arXiv preprint arXiv:math/0703890},
  year   = {2020}
}

Comments

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 Poincar\'e duality pair, our decomposition behaves like the JSJ-decomposition of a 3-manifold

R2 v1 2026-07-22T17:53:28.722Z