Boundaries and JSJ Decompositions of CAT(0)-Groups
By Panos Papasoglu, E. Swenson. 2007
57 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/74450bf059c99852a630b30bb33c9c1d91debdad
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In Geometry and Topology
- J. Porti
- Michael Kapovich
- B. Leeb
- Anna Wienhard
- Jean-Marc Schlenker
- Bruce Kleiner
- Cornelia Drutu
- M. Boileau
In Mathematical Physics
- Michael Kapovich
- B. Leeb
- J. Porti
- Anna Wienhard
- Olivier Y Guichard
- Andr'es Sambarino
- M. B. Pozzetti
- Bruce Kleiner
Citations in the corpus
- Dynamics on flag manifolds: domains of proper discontinuity and cocompactness (2013, background): “This kind of convergence type dynamical behavior had been observed, in the general setting of proper CAT(0) spaces, by Karlsson [Kar, Thm. 1] and Papasoglu and Swenson [PS, Thm. 4], see also the first version of this paper [KLP1, Thm. 1.1 and §6.1].”