Ariadna Fossas (2014)

# Thompson’s Group T, Undistorted Free Groups and Automorphisms of the Flip Graph

In: Extended Abstracts Fall 2012, ed. by González-Meneses, Juan and Lustig, Martin and Ventura, Enric, pp. 45–49, Springer International Publishing. Trends in Mathematics. (ISBN: 978-3-319-05487-2, 978-3-319-05488-9).

In this paper we present combinatorial and geometric results about Thompson’s group T by comparing multiple viewpoints of the same object and their interactions (see [3] for an introduction to Thompson’s groups). First, we find a non distorted subgroup of T isomorphic to the free non abelian group of rank 2 by using both the combinatorial version of T in terms of equivalence classes of tree pair diagrams, and Thurston’s approach of T in terms of piecewise TeXmathit\PSL\\_\2\(mathbb\Z\) homeomorphisms of the real projective line (see [7, 10, 13]). Second, we study the action of T on a locally infinite graph TeXmathcal\C\ˆ\1\ that can be seen as a generalisation of the flip graph (see, for example, [9]) for an infinitely sided convex polygon. The automorphism group of TeXmathcal\C\ˆ\1\ is an extension of Thompson’s group T.An Undistorted F2 in Thompson’s Group TThe piecewise linear Thompson’s group T is the group of orientation-preserving piecewise linear homeomorphisms of th

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