JSJ-splittings for finitely presented groups over slender groups
- 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 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.