Author
Papasoglu, P
Swenson, E
Last updated
2024-02-17T09:19:29.017+00:00
Abstract
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 $\frac {3\pi} 2$ then it is infinite and G contains a free
subgroup of rank 2.
Symplectic ID
191446
Download URL
http://arxiv.org/abs/math/0701618v2
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Publication type
Journal Article
Publication date
22 Jan 2007
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