Parallelogram decompositions and generic surfaces in \(\mathcal H^{\text{hyp}}(4)\)

DOI10.2140/gt.2011.15.1707zbMath1238.57020arXiv1012.0994OpenAlexW3123072842MaRDI QIDQ640346

Duc-Manh Nguyen

Publication date: 18 October 2011

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.0994

zbMATH Keywords

translation surfacesquare tiled surfacemoduli space of Abelian differentialssingular flat structureVeech surface

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (6)

Translation surfaces and the curve graph in genus two ⋮ The boundary of an affine invariant submanifold ⋮ Non-Veech surfaces in \(\mathcal H^{\mathrm{hyp}}(4)\) are generic ⋮ The field of definition of affine invariant submanifolds of the moduli space of abelian differentials ⋮ Existence of closed geodesics through a regular point on translation surfaces ⋮ Classification of higher rank orbit closures in \(\mathcal{H}^{\mathrm{odd}}(4)\)

Cites Work

• Completely periodic directions and orbit closures of many pseudo-Anosov Teichmüller discs in \(\mathrm{Q}(1,1,1,1)\).
• Moduli spaces of quadratic differentials
• The Arnoux-Yoccoz Teichmüller disc
• Algebraically periodic translation surfaces
• Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
• Interval exchange transformations and measured foliations
• On the density of Strebel differentials
• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Dynamics of \(\text{SL}_2(\mathbb R)\) over moduli space in genus two
• On the geometry and dynamics of diffeomorphisms of surfaces
• Veech surfaces and complete periodicity in genus two
• Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
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