CAT(0) geometry for the Thompson Group

Details CAT(0) geometry for the Thompson Group CAT(0) geometry for the Thompson Group

2012-03-26

arxiv.org/abs/1203.5749v1

Mathematics

Group Theory

PhD Thesis at EPFL (submitted as such in November 2011)

Scientific paper

We investigate Farley's CAT(0) cubical model for Thompson's group F (we adopt the classical language of F, using binary trees and piecewise linear maps). Main results include: in general, Thompson's group elements are parabolic; we find simple, exact formulas for the CAT(0) translation lengths, in particular the elements of F are ballistic and uniformly bounded away from zero; there exist flats of any dimension and we construct explicitly many of them; we reveal large regions in the Tits Boundary, for example the positive part of a non-separable Hilbert sphere, but also more complicated objects. En route, we solve several open problems proposed in Farley's papers.

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