Invariants of translation surfaces

By Pascal Hubert, Thomas A. Schmidt. 2001

47 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6a8ec30f2cd4d6d2e434efc9a03c5edd94c28b54

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. G. Forni
2. A. Eskin
3. A. Zorich
4. A. Wright
5. H. Masur
6. Carlos Matheus
7. Gabriela Schmithuesen
8. Patrick Hooper

In Mathematical Physics

1. A. Zorich
2. A. Eskin
3. G. Forni
4. A. Wright
5. H. Masur
6. Dawei Chen
7. Carlos Matheus
8. Martin Möller

Citations in the corpus

• Teichmuller curves, triangle groups, and Lyapunov exponents (2005, unknown): “group ∆(m,n,∞) are geometrically primitive, Theorem 2.6 of [M¨o04] does not exclude that there are other primitive Veech surfaces with the same affine group. Such examples are provided by Theorem 3’ of [HuSc01] for n= ∞. By Remark 2.3 we know a rank 2rsubvariation of Hodge structures of the family of ”
• Grid graphs and lattice surfaces (2008, methodology): “This theorem was used in [ HS01 , remark 7] to show that +(2;m;1) can not arise as”
• Moduli spaces of Abelian differentials: The principal boundary, counting problems, and the Siegel–Veech constants (2002, methodology): “These lists have proved to be important invariants of such orbifolds: in [ HuS ] they are used to give an example of different Veech surfaces (with different Teichm¨uller discs) sharing isomorphic Veech groups.”
• On the boundary of Teichmüller disks in Teichmüller and in Schottky space (2007, background): “Later more examples with triangle groups as Veech groups were found, see [20] for a comprehensive overview and [6] for recent results.”
• Cylinder deformations in orbit closures of translation surfaces (2013, background): “Besides the examples mentioned above (following Theorem 1.7), the only additional currently known examples are closed orbits: the Veech–Ward–Bouw–Möller curves (see Veech [25], Ward [27], Bouw and Möller [3] and Wright [28]), as well as two sporadic examples due to Vorobets and to Kenyon and Smillie”
• An extraordinary origami curve (2005, methodology): “attracted a lot of attention, partly because of their relation to rational billiards, see e.g. [McM] and references therein; a survey of examples defining primitive Teichmu¨ller curves can be found in [HuSc]. Another topic of interest is the action of the absolute Galois group of the rationals on the”
• A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle (2010, background): “lgebraically primitive, given by Prym eigenforms in genus 3 and 4, was discovered by C. McMullen [Mc2]. The Prym class contains an example discovered earlier by M. Möller [Mö1],§2 (studied earlier in [HuS]). In genus 3 it appears that most geometrically primitive Veech surfaces are not algebraically”