Geodesic
Denominator bounds in Thompson-like groups and flows
Danny Calegari1
1California Institute of Technology, Pasadena, United States
Groups, geometry, and dynamics, Tome 1 (2007) no. 2, pp. 101-109

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DOI

Let T denote Thompson's group of piecewise 2-adic linear homeomorphisms of the circle. Ghys and Sergiescu showed that the rotation number of every element of T is rational, but their proof is very indirect. We give here a short, direct proof using train tracks, which generalizes to elements of PL+(S1) with rational break points and derivatives which are powers of some fixed integer, and also to certain flows on surfaces which we call Thompson-like. We also obtain an explicit upper bound on the smallest period of a fixed point in terms of data which can be read off from the combinatorics of the homeomorphism.
DOI : 10.4171/ggd/6
Classification : 37-XX, 00-XX
Mots-clés : Thompson's group, rotation number, rationality

Danny Calegari  1

1 California Institute of Technology, Pasadena, United States 
Danny Calegari. Denominator bounds in Thompson-like groups and flows. Groups, geometry, and dynamics, Tome 1 (2007) no. 2, pp. 101-109. doi: 10.4171/ggd/6
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