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arxiv: 1310.5364 · v1 · pith:EMFUIM2Anew · submitted 2013-10-20 · 🧮 math.DS

Stable Type of the Mapping Class Group

Ilya Gekhtman This is my paper
classification 🧮 math.DS
keywords stabletypeclassgrouplambdamappingsomeaction
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We use dynamics of the Teichm$\ddot{\mathrm{u}}$ller geodesic flow to show that the action of the mapping class group on the space of projective measured foliations has stable type $III_{\lambda}$ for some $\lambda>0$. We do this by generalizing a criterion due to Bowen for a number to be in the stable ratio set, and proving some Patterson-Sullivan type results for the Thurston measure on $PMF$.

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