Rotation numbers in Thompson–Stein groups and applications

Rotation numbers in Thompson–Stein groups and applications

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...

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Veröffentlicht in:Geometriae dedicata 2008-02, Vol.131 (1), p.49-71
1. Verfasser: Liousse, Isabelle
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Zusammenfassung: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 Diff 9 ( S 1 ).
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-007-9216-y