Transactions of the American Mathematical Society

Author(s): Peter Scott; Gadde A. Swarup
Journal: Trans. Amer. Math. Soc. 353 (2001), 4973-5001.
MSC (2000): Primary 57M07, 57N10, 20E06
Posted: July 25, 2001
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We introduce the notion of a `canonical' splitting over $\mathbb{Z}$ or $\mathbb{Z}\times\mathbb{Z}$ 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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 57M07, 57N10, 20E06

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: 10.1090/S0002-9947-01-02871-9
PII: S 0002-9947(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
Posted: July 25, 2001
Additional Notes: The first author was partially supported by NSF grant DMS 034681.
Copyright of article: Copyright 2001, American Mathematical Society

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