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ISSN 1079-6762

 

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: 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: http://dx.doi.org/10.1090/S1079-6762-02-00102-6
PII: S 1079-6762(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