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Boundaries and JSJ Decompositions of CAT(0)-Groups

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Abstract

Let G be a one-ended group acting discretely and co-compactly on a CAT(0) space X. We show that ∂X has no cut points and that one can detect splittings of G over two-ended groups and recover its JSJ decomposition from ∂X.

We show that any discrete action of a group G on a CAT(0) space X satisfies a convergence type property. This is used in the proof of the results above but it is also of independent interest. In particular, if G acts co-compactly on X, then one obtains as a corollary that if the Tits diameter of ∂X is bigger than 3π/2 then it is infinite and G contains a free subgroup of rank 2.

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Authors and Affiliations

  1. Mathematics Department, University of Athens, Athens, 157 84, Greece

    Panos Papasoglu

  2. Mathematics Department, Brigham Young University, Provo, UT, 84602, USA

    Eric Swenson

Authors
  1. Panos Papasoglu
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  2. Eric Swenson
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Correspondence to Panos Papasoglu.

Additional information

This work is co-funded by European Social Fund and National Resources (EPEAEK II) PYTHAGORAS.

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Papasoglu, P., Swenson, E. Boundaries and JSJ Decompositions of CAT(0)-Groups. Geom. Funct. Anal. 19, 558–590 (2009). https://doi.org/10.1007/s00039-009-0012-8

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  • DOI: https://doi.org/10.1007/s00039-009-0012-8

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