Teichmuller curves, triangle groups, and Lyapunov exponents
By Irene I. Bouw, Martin Moeller. 2005
165 citations recorded by the source corpus.
We construct a Teichmuller curve uniformized by a Fuchsian triangle group commensurable to �(m, n, ∞) for every m, n ≤ ∞. In most cases, for example when m 6 n and m or n is odd, the uniformizing group is equal to the triangle group �(m, n, ∞). Our construction includes the Teichmuller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. For small m, we find billiard tables that generate these Teich- muller curves. We interpret some of the so-called Lyapunov exponents of the Kontsevich-Zorich cocycle as normalized degrees of a natural line bundle on a Teichmuller curve. We determine the Lyapunov exponents for the Teichmuller curves we construct.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/73ef231eced569560968dcfaa360dfdf6741e5f0
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
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- Patrick Hooper
- Frank Herrlich
- Alexander I. Bufetov
- A. Eskin
Citations in the corpus
- SQUARE-TILED CYCLIC COVERS (2010, methodology): “In a similar way we can check that α(c1,c2) and β are holomorphic (see [5], [6], [12] for more details).”
- Grid graphs and lattice surfaces (2008, methodology): “m;n; em;n). Compare the following to [ BM06 , theorem 5.15].”
- 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.”