Translation lengths of pseudo-Anosov mapping classes
Philipp Bader (University of Glasgow)
Monday 28th October 16:00-17:00 Maths 311B
Abstract
The mapping class group of a closed surface S acts on the Teichmüller space, as well as the curve graph of S. Pseudo-Anosov elements act in a particularly nice way: for a pseudo-Anosov, there exists a geodesic in both Teichmüller space and the curve graph, such that (a power of) the pseudo Anosov preserves that geodesic and acts on it by translation. Measuring these translation lengths yields two real numbers as invariants for the pseudo-Anosov.
In this talk, we will explore the relationship between the two invariants. In particular, we'll show the different behaviours of the two for a family of pseudo-Anosovs. In order to define this family, we introduce the notion of a flat structure on S and discuss Rauzy-Veech induction. We then present techniques in order to compute the translation lengths.
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