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We find canonical decompositions for finitely presented groups which essentially specialise 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 of a family of almost invariant subsets of a group. An almost invariant set is an analogue of an immersion.

Copyright 2002 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 08 (2002), pp. 20-28
• Publisher Identifier: S 1079-6762(02)00102-6
• 2000 Mathematics Subject Classification. Primary 20E34; Secondary 57N10, 57M07
• Key words and phrases. Graph of groups, almost invariant set, characteristic submanifold
• Received by editors May 1, 2002
• Received by editors in revised form July 23, 2002
• Posted on September 6, 2002
• Communicated by Walter Neumann
• Comments (When Available)

Peter Scott

Mathematics Department, University of Michigan, Ann Arbor, MI 48109, USA

E-mail address: pscott@umich.edu

Gadde A. Swarup

Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia

E-mail address: gadde@ms.unimelb.edu.au

First author partially supported by NSF grants DMS 034681 and 9626537.