The Kontsevich–Zorich cocycle over Veech–McMullen family of symmetric translation surfaces

Artur Avila; Carlos Matheus; Jean-Christophe Yoccoz

doi:10.3934/jmd.2019002

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2019, Volume 14: 21-54. Doi: 10.3934/jmd.2019002

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The Kontsevich–Zorich cocycle over Veech–McMullen family of symmetric translation surfaces

1.
IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil
2.
Centre de Mathématiques Laurent Schwartz, CNRS (UMR 7640), École Polytechnique, 91128 Palaiseau, France
3.
Collège de France, 3 Rue d'Ulm, Paris, Cedex 05, France

Received: December 20, 2017

Revised: July 12, 2018

Published: March 2019

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Abstract

We describe the Kontsevich–Zorich cocycle over an affine invariant orbifold coming from a (cyclic) covering construction inspired by works of Veech and McMullen. In particular, using the terminology in a recent paper of Filip, we show that all cases of Kontsevich–Zorich monodromies of $ SU(p,q) $ type are realized by appropriate covering constructions.

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Mathematics Subject Classification: Primary: 37D40; Secondary: 37C85.

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References

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