Regular neighbourhoods and canonical decompositions for groups

Authors:
Peter Scott and Gadde A. Swarup

Journal:
Electron. Res. Announc. Amer. Math. Soc. **8** (2002), 20-28

MSC (2000):
Primary 20E34; Secondary 57N10, 57M07

Published electronically:
September 6, 2002

MathSciNet review:
1928498

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Abstract | References | Similar Articles | Additional Information

Abstract: 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.

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Additional Information

**Peter Scott**

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

Email:
pscott@umich.edu

**Gadde A. Swarup**

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

Email:
gadde@ms.unimelb.edu.au

DOI:
https://doi.org/10.1090/S1079-6762-02-00102-6

Keywords:
Graph of groups,
almost invariant set,
characteristic submanifold

Received by editor(s):
May 1, 2002

Received by editor(s) in revised form:
July 23, 2002

Published electronically:
September 6, 2002

Additional Notes:
First author partially supported by NSF grants DMS 034681 and 9626537

Communicated by:
Walter Neumann

Article copyright:
© Copyright 2002
American Mathematical Society