Regular Neighbourhoods and Canonical Decompositions for Groups

2001/10/31 by Peter Scott, Gadde Swarup
Mathematics · #math.GR #math.GT #msc:20F65 #msc:57M07 #msc:20E34

paper · pdf

published as Asterisque 289 (2003) · 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

arxiv created 2001/12/20 · arxiv updated 2009/11/30

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.

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