GL2ℝ–invariant measures in marked strata : generic marked points, Earle–Kra for strata and illumination

Apisa, Paul

doi:10.2140/gt.2020.24.373

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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

Geometry & Topology 24 (2020) 373–408

DOI: 10.2140/gt.2020.24.373

Abstract

We show that nontrivial $GL (2, ℝ)$ –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.

Keywords

dynamics on Teichmüller space, flat surfaces, translation surfaces

Mathematical Subject Classification 2010

Primary: 30F60, 32G15, 37F30

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

Authors

Paul Apisa
Department of Mathematics University of Chicago Chicago, IL United States	Department of Mathematics Yale University New Haven, CT United States

Volume 24, issue 1 (2020)