Abstract
We study the rationality properties of rotation numbers for some groups of piecewise linear homeomorphisms of the circle, the Thompson–Stein groups. We prove that for many Thompson–Stein groups the outer automorphism group has order 2. As another application, we construct Thompson–Stein groups which do not admit non trivial representations in Diff9(S 1).
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Liousse, I. Rotation numbers in Thompson–Stein groups and applications. Geom Dedicata 131, 49–71 (2008). https://doi.org/10.1007/s10711-007-9216-y
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DOI: https://doi.org/10.1007/s10711-007-9216-y