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

Authors :: Jean-Christophe Yoccoz
Carlos Matheus
Artur Avila
University of Zurich
Instituto Nacional de Matemática Pura e Aplicada (IMPA)
Instituto Nacional de matematica pura e aplicada
Laboratoire Analyse, Géométrie et Applications (LAGA)
Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13)
Collège de France (CdF (institution))
Source :: Journal of modern dynamics, Journal of modern dynamics, American Institute of Mathematical Sciences, 2019, 14 (1), pp.21-54. ⟨10.3934/jmd.2019002⟩
Publication Year :: 2019
Publisher :: American Institute of Mathematical Sciences (AIMS), 2019.
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 \begin{document}$ SU(p,q) $\end{document} type are realized by appropriate covering constructions.

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