The Action of Thompson's Group on a CAT(0) Boundary

Details The Action of Thompson's Group on a CAT(0) Boundary The Action of Thompson's Group on a CAT(0) Boundary

2006-04-04

arxiv.org/abs/math/0604077v1

Mathematics

Group Theory

33 pages, 28 figures

Scientific paper

One way to show that Thompson's group F is non-amenable is to exhibit an action of F on a locally compact CAT(0) space X containing no F-invariant flats and having no global fixed points in its boundary-at-infinity. We study the actions of Thompson's groups F, T, and V on the boundaries-at-infinity of proper CAT(0) cubical complexes. In particular, we show that Thompson's groups T and V act without fixing any points in the boundaries of their CAT(0) cubical complexes. This in particular gives another proof of the well-known fact that these groups are non-amenable. We obtain a partial description of the fixed set for F: Thompson's group F fixes an arc in the boundary of its cubical complex. We leave open the possibility that there are more fixed points, but describe a region of the boundary which must contain all of the others.

Affiliated with

Also associated with

No associations

Rating

The Action of Thompson's Group on a CAT(0) Boundary 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 The Action of Thompson's Group on a CAT(0) Boundary, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Action of Thompson's Group on a CAT(0) Boundary will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-501253