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

Artur Avila; Carlos Matheus; Jean Christophe Yoccoz

doi:10.3934/jmd.2019002

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

Artur Avila, Carlos Matheus, Jean Christophe Yoccoz

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	21-54
Number of pages	34
Journal	Journal of Modern Dynamics
Volume	14
DOIs	https://doi.org/10.3934/jmd.2019002
Publication status	Published - 1 Jan 2019

Keywords

Complex reflection group
Cyclic covers
Hyperelliptic Rauzy diagrams
Teichmüller dynamics
Veech-McMullen families

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10.3934/jmd.2019002

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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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AU - Yoccoz, Jean Christophe

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KW - Complex reflection group

KW - Cyclic covers

KW - Hyperelliptic Rauzy diagrams

KW - Teichmüller dynamics

KW - Veech-McMullen families

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DO - 10.3934/jmd.2019002

M3 - Article

AN - SCOPUS:85067481736

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ER -

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

Abstract

Keywords

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