Regular Neighbourhoods and Canonical Decompositions for Groups

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.

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

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