Veech surfaces and complete periodicity in genus two

By Kariane Calta. 2004

206 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9ea7725b89fca8d9353da9343f33547e840b527a

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The field of definition of affine invariant submanifolds of the moduli space of abelian differentials (2012, background): “All of the possible orbit closures (affine invariant manifolds) listed had been previously studied by both McMullen [23] and Calta [3].”
Euler characteristics of Teichmüller curves in genus two (2006, methodology): “owed that D10 and the WD for D nonsquare are in fact all of the primitive Teichmu¨ller curves in M2 generated by an Abelian diﬀerential. Teichmu¨ller curves in genus two were also studied by Calta in [Cal04], using the Kenyon-Smillie invariant introduced in [KS00]. 13 Associated to every known SL2Ro”
Teichmüller curves in genus two: Torsion divisors and ratios of sines (2006, result): “For additional results related to Teichm¨uller curves in genus two, see [V], [GJ], [EMS], [HS], [HL], and [ Ca ].”
ON ARITHMETIC CURVES IN THE MODULI SPACES OF CURVES (2005, background): “One should also notice that prior to [49] and [8], all monodromy groups that had been computed were triangular.”
Teichmüller curves in genus two: Discriminant and spin (2005, background): “See [EMS] and [HL] for additional results on the curves Wd2, and [V1], [V2], [Vo], [Wa], [KS], [Pu], [GJ], [EO], and [ Ca ] for more on Teichm¨uller curves.”
On groups generated by two positive multi-twists: Teichmuller curves and Lehmer's number (2003, background): “ttice polygons is an interesting problem which has received much attention (see eg Veech [56], [57], Harvey [27], Gutkin and Judge [25], Kenyon and Smillie [32], Puchta [48], McMullen [44], and Calta [13]). Our second main theorem provides a complete classiﬁcation for a certain class of Teichmu¨ller”
Beyond Sturmian sequences: coding linear trajectories in the regular octagon (2011, background): “Calta [4] and McMullen [16] showed that in appropriate coordinates these are just the directions with slopes in the field Q( √ 2) (see also [3]).”
A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle (2010, background): “ measure is afﬁne, has been recently announced by A. Eskin and M. Mirzakh ani [EM]. For the genus two case, all SL(2,R)-invariant probability measures were classiﬁed by C. McMullen [Mc1] and K. Calta [Ca] and are known to be afﬁne. Next we recall the notion of a completely periodic Lagrangian measur”
Introduction to Teichm\"uller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards (2013, background): “res are algebraic. If it is true, this conjecture would provide a non-homogenous counterpart to Ratner’s theorems [68] on unipotent actions in homogenous spaces. After the celebrated work of K. Calta [15] and C. McMullen [65], there is a complete classication of all SL(2;R)-invariant measures in gen”