An extraordinary origami curve

By Frank Herrlich, Gabriela Schmithuesen. 2005

73 citations recorded by the source corpus.

We study the origami W defined by the quaternion group of order 8 and its Teichmüller curve C (W) in the moduli space M3. We prove that W has Veech group SL2(ℤ), determine the equation of the family over C (W) and find several further properties. As main result we obtain infinitely many origami curves in M3 that intersect C (W). We also present a combinatorial description of these origamis. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f10303d8f31d49c7a45b3e04c315058eff23290e

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Introduction to Teichm\"uller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards (2013, background): “ove example seems rather special. In the literature, the square-tiled surface (M 3( 1;0;1;1);! EW) in the support of EWwas named Eierlegende Wollmilchsau by F. Herrlich, M. Moller, G. Schmithusen [41] because it has peculiar algebro-geometrical properties (see [41]) in addition to its totally degen”
Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication (2007, background): “s section we give an additional group E4 of M1-automorphisms such that G4 and E4 generate an extended M1-automorphism group G¯4. Moreover we will make some remarks about G¯ 4 and E4. We obtain due to [24], Proposition 9 and the notations of [24], Section 2: Proposition 9.5.1. The family C2 has a gro”
On the boundary of Teichmüller disks in Teichmüller and in Schottky space (2007, background): “In genus 3 there is even an explicit example of an origami curve that is intersected by infinitely many others, see [ 18 ].”
A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle (2010, unknown): “COCYCLE 7 SL(2,R)-invariant probability measure supported on the closedSL(2,R)- orbit of an ‘exceptionally symmetric’ translation surface of genus 3, often called the Eierlegende Wollmilchsau surface [HeS]. For such a measure the Kontsevich–Zorich spectrum is maximally degenerate (all non-trivial ex”
SQUARE-TILED CYCLIC COVERS (2010, background): “in Forni’s example, found independently by F. Herrlich, M. Möller and G. Schmithuesen, is very peculiar, very symmetric, and has so manyremarkablepropertiesthathasbeenaptlynamedEierlegendeWollmilchsau[20]. LaterG.ForniandC.Matheusannouncedinthepreprint[17]asecond example of the same kind in genus fo”