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

2017/10/31 by Artur Avila, Avila, Artur, Carlos Matheus +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.DS

paper · pdf · doi:10.48550/arxiv.1710.11323

32 pages, no figures. Final version based on the referee report. To appear in Veech special volume of Journal of Modern Dynamics

arxiv created 2018/08/02 · arxiv updated 2018/08/03

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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