Boundaries and JSJ decompositions of CAT(0)-groups

Details Boundaries and JSJ decompositions of CAT(0)-groups Boundaries and JSJ decompositions of CAT(0)-groups

2007-01-22

arxiv.org/abs/math/0701618v2

Mathematics

Group Theory

minor corrections,38 pages, 2 figures, to appear in GAFA

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Boundaries and JSJ decompositions of CAT(0)-groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Boundaries and JSJ decompositions of CAT(0)-groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Boundaries and JSJ decompositions of CAT(0)-groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-516822