Canonical splittings of groups and 3-manifolds

Authors:
Peter Scott and Gadde A. Swarup

Journal:
Trans. Amer. Math. Soc. **353** (2001), 4973-5001

MSC (2000):
Primary 57M07, 57N10, 20E06

DOI:
https://doi.org/10.1090/S0002-9947-01-02871-9

Published electronically:
July 25, 2001

MathSciNet review:
1852090

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We introduce the notion of a `canonical' splitting over or for a finitely generated group . We show that when happens to be the fundamental group of an orientable Haken manifold with incompressible boundary, then the decomposition of the group naturally obtained from canonical splittings is closely related to the one given by the standard JSJ-decomposition of . This leads to a new proof of Johannson's Deformation Theorem.

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Additional Information

**Peter Scott**

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

Email:
pscott@math.lsa.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/S0002-9947-01-02871-9

Keywords:
3-manifold,
characteristic submanifold,
Deformation Theorem,
ends of groups,
intersection number,
JSJ decomposition,
splittings of groups

Received by editor(s):
August 12, 2000

Received by editor(s) in revised form:
April 9, 2001

Published electronically:
July 25, 2001

Additional Notes:
The first author was partially supported by NSF grant DMS 034681.

Article copyright:
© Copyright 2001
American Mathematical Society