Regular Neighbourhoods and Canonical Decompositions for Groups
Group Theory
2007-05-23 v2 Geometric Topology
Abstract
We find canonical decompositions for finitely presented groups which specialize to the classical JSJ-decomposition when restricted to the fundamental groups of Haken manifolds. The decompositions that we obtain are invariant under automorphisms of the group. A crucial new ingredient is the concept of a regular neighbourhood for a finite family of almost invariant subsets of a group. An almost invariant set is an analogue of an immersion.
Cite
@article{arxiv.math/0110210,
title = {Regular Neighbourhoods and Canonical Decompositions for Groups},
author = {Peter Scott and Gadde Swarup},
journal= {arXiv preprint arXiv:math/0110210},
year = {2007}
}
Comments
First version: 124 pages. This is a preliminary version. Second version: 155 pages. Added new sections, more details and more examples. Reorganised parts of paper, and improved exposition