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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
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 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.

Keywords

Small Subgroup Ambient Group Slender Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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: mjd@maths.soton.ac.uk, sageev@andromeda.rutgers.edu)XX

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