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$\mathrm{GL}_2
\mathbb{R}$–invariant measures in marked strata: generic
marked points, Earle–Kra for strata and illumination
Paul Apisa |
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Geometry & Topology 24 (2020) 373–408
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Abstract |
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We show that nontrivial –invariant point markings for translation surfaces in strata of abelian differentials exist only when the translation surface belongs to a hyperelliptic component. As an application, we establish constraints on sections of the universal curve restricted to orbifold covers of subvarieties of the moduli space of Riemann surfaces that contain a Teichmüller disk. We also solve the finite blocking problem for generic translation surfaces. |
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Keywords
dynamics on Teichmüller space, flat surfaces, translation
surfaces
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Mathematical Subject Classification 2010
Primary: 30F60, 32G15, 37F30
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References |
Publication
Received: 6 September 2018
Revised: 29 March 2019
Accepted: 18 June 2019
Published: 25 March 2020
Proposed: Benson Farb
Seconded: Anna Wienhard, Jean-Pierre Otal
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Authors |
| Paul Apisa | |
| Department of Mathematics University of Chicago Chicago, IL United States |
Department of Mathematics Yale University New Haven, CT United States |
