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JSJ-splittings for fintely presented groups over slender groups

JSJ-splittings for fintely presented groups over slender groups
JSJ-splittings for fintely 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.
0020-9910
25-44
Dunwoody, M.J.
ab9cba4b-1c90-4353-ad26-2b497d25cce3
Sageev, M.E.
db1f3994-24d6-4d46-bcb3-6a66309970ce
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 fintely presented groups over slender groups. Inventiones Mathematicae, 135 (1), 25-44. (doi:10.1007/s002220050278).

Record type: Article

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

Identifiers

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 Jul 2019 19:08

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