Inventiones mathematicae

, Volume 135, Issue 1, pp 25–44 | Cite as

JSJ-splittings for finitely presented groups over slender groups

  • M. J. Dunwoody
  • M. E. Sageev


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.


Small Subgroup Ambient Group Slender Group 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • M. J. Dunwoody
    • 1
  • M. E. Sageev
    • 2
  1. 1.Faculty of Mathematical Studies, University of Southampton, Southampton, SO17 1BJ, UKGB
  2. 2.Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102 (email:,

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