ARTICLE

Inventiones mathematicae

, Volume 135, Issue 1, pp 25-44

JSJ-splittings for finitely presented groups over slender groups

  • M. J. DunwoodyAffiliated withFaculty of Mathematical Studies, University of Southampton, Southampton, SO17 1BJ, UK
  • , M. E. SageevAffiliated withDepartment of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102 (email: mjd@maths.soton.ac.uk, sageev@andromeda.rutgers.edu)

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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 ZZ 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.