2007/01/22 by Panos Papasoglu, Papasoglu, Panos, Eric Swenson +1
Mathematics · #20E06 #20E34 #20F67 #57M07 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG) #math.GR #math.GT #math.MG #msc:20E06 #msc:20E34 #msc:20F67 #msc:57M07
paper · pdf · doi:10.48550/arxiv.math/0701618
minor corrections,38 pages, 2 figures, to appear in GAFA
openalex publication_date 2007/01/22 · arxiv created 2008/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a one-ended group acting discretely and co-compactly on a CAT(0) space X. We show that the boundary of X has no cut points and that one can detect splittings of G over two-ended groups and recover its JSJ decomposition from the boundary. 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 the boundary of X is bigger than \frac 3π 2 then it is infinite and G contains a free subgroup of rank 2.