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BOUNDARIES AND JSJ DECOMPOSITIONS OF CAT(0)-GROUPS (2007)
| Citations: | 11 - 0 self |
BibTeX
@MISC{Papasoglu07boundariesand,
author = {Panos Papasoglu and Eric Swenson},
title = {BOUNDARIES AND JSJ DECOMPOSITIONS OF CAT(0)-GROUPS},
year = {2007}
}
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Abstract
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. 1.
