Inventiones mathematicae

, Volume 135, Issue 1, pp 25–44

JSJ-splittings for finitely presented groups over slender groups


  • M. J. Dunwoody
    • Faculty of Mathematical Studies, University of Southampton, Southampton, SO17 1BJ, UK
  • M. E. Sageev
    • Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102 (email:,

DOI: 10.1007/s002220050278

Cite this article as:
Dunwoody, M. & Sageev, M. Invent math (1999) 135: 25. doi:10.1007/s002220050278


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.

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© Springer-Verlag Berlin Heidelberg 1999