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