6 Teichmüller Curves , Triangle Groups , and Lyapunov Exponents
نویسندگان
چکیده
We construct a Teichmüller curve uniformized by the Fuchsian triangle group ∆(m, n, ∞) for every m < n ≤ ∞. Our construction includes the Teichmüller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. For small m, we find bil-liard tables that generate these Teichmüller curves. We interprete some of the so-called Lyapunov exponents of the Kontsevich–Zorich cocycle as normalized degrees of a natural line bundle on a Teichmüller curve. We determine the Lyapunov exponents for the Teichmüller curves we construct.
منابع مشابه
Teichm¨uller Curves, Triangle Groups, and Lyapunov Exponents
We construct a Teichmüller curve uniformized by the Fuchsian triangle group ∆(m, n, ∞) for every m < n ≤ ∞. Our construction includes the Teichmüller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. We interprete some of the so-called Lyapunov exponents of the Kontsevich–Zorich cocycle as normalize...
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