JSJ-splittings for finitely presented groups over slender groups
JSJ-splittings for finitely presented groups over slender groups
We generalize the JSJ-splitting of Rips and Sela to give decompositions of finitely presented groups which capture splittings over certain classes of small subgroups. Such classes include the class of all 2-ended groups and the class of all virtually Z]Z groups. The approach, called "track zipping", is relatively elementary, and differs from the Rips-Sela approach in that it does not rely on the theory of R-trees but rather on an understanding of certain embedded 1-complexes (called patterns) in a presentation 2-complex for the ambient group.
25-44
Dunwoody, M.J.
ab9cba4b-1c90-4353-ad26-2b497d25cce3
Sageev, M.E.
db1f3994-24d6-4d46-bcb3-6a66309970ce
1999
Dunwoody, M.J.
ab9cba4b-1c90-4353-ad26-2b497d25cce3
Sageev, M.E.
db1f3994-24d6-4d46-bcb3-6a66309970ce
Dunwoody, M.J. and Sageev, M.E.
(1999)
JSJ-splittings for finitely presented groups over slender groups.
Inventiones Mathematicae, 135 (1), .
(doi:10.1007/s002220050278).
Abstract
We generalize the JSJ-splitting of Rips and Sela to give decompositions of finitely presented groups which capture splittings over certain classes of small subgroups. Such classes include the class of all 2-ended groups and the class of all virtually Z]Z groups. The approach, called "track zipping", is relatively elementary, and differs from the Rips-Sela approach in that it does not rely on the theory of R-trees but rather on an understanding of certain embedded 1-complexes (called patterns) in a presentation 2-complex for the ambient group.
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Published date: 1999
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Local EPrints ID: 29896
URI: http://eprints.soton.ac.uk/id/eprint/29896
ISSN: 0020-9910
PURE UUID: cc47ccbd-93da-45ac-8f82-5d25c7b5e26a
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Date deposited: 22 Dec 2006
Last modified: 15 Mar 2024 07:36
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Author:
M.J. Dunwoody
Author:
M.E. Sageev
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