Geometric and Functional Analysis

, Volume 19, Issue 2, pp 558–590

Boundaries and JSJ Decompositions of CAT(0)-Groups

Authors

    • Mathematics DepartmentUniversity of Athens
  • Eric Swenson
    • Mathematics DepartmentBrigham Young University
Article

DOI: 10.1007/s00039-009-0012-8

Cite this article as:
Papasoglu, P. & Swenson, E. Geom. Funct. Anal. (2009) 19: 558. doi:10.1007/s00039-009-0012-8

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.

Keywords and phrases

Boundarycut pointJSJ decompositionclosing lemma

2000 Mathematics Subject Classification

20F6720E0620E3457M07

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009