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


Avila, Artur; Matheus, Carlos; Yoccoz, Jean-Christophe (2019). The Kontsevich–Zorich cocycle over Veech–McMullen family of symmetric translation surfaces. Journal of Modern Dynamics, 14(1):21-54.

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.

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Physical Sciences > Algebra and Number Theory
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Algebra and Number Theory, Applied Mathematics, Analysis
Language:English
Date:1 January 2019
Deposited On:28 Jun 2019 08:42
Last Modified:29 Jul 2020 10:54
Publisher:American Institute of Mathematical Sciences (A I M S Press)
ISSN:1930-532X
OA Status:Green
Publisher DOI:https://doi.org/10.3934/jmd.2019002

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