Volume 25, issue 6 (2021)

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Marked points on translation surfaces

Paul Apisa and Alex Wright

Geometry & Topology 25 (2021) 2913–2961
Abstract

We show that all GL+(2, ) equivariant point markings over orbit closures of translation surfaces arise from branched covering constructions and periodic points, completely classify such point markings over strata of quadratic differentials, and give applications to the finite blocking problem.

Keywords
translation surfaces, abelian differentials, Teichmüller dynamics
Mathematical Subject Classification 2010
Primary: 32G15, 37F30
References
Publication
Received: 6 December 2019
Revised: 30 August 2020
Accepted: 8 October 2020
Published: 30 November 2021
Proposed: Mladen Bestvina
Seconded: David M Fisher, Bruce Kleiner
Authors
Paul Apisa
Department of Mathematics
Yale University
New Haven, CT
United States
Alex Wright
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States