Teichmuller curves, triangle groups, and Lyapunov exponents
Teichmuller curves, triangle groups, and Lyapunov exponents
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DOI：
10.4007/annals.2010.172.139
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发表时间：
2005-11
影响因子：
4.9
通讯作者：
I. Bouw;Martin Moeller
中科院分区：
文献类型：
--
作者：
I. Bouw;Martin Moeller
本文构造了一条由Fuchsian三角形群一致化的Teichmuller曲线，对任意m，n ≤ ∞，该三角形群可满足λ（m，n，∞）.在大多数情况下，例如当m 6 n且m或n为奇数时，均匀化群等于三角形群（m，n，∞）。我们的建设包括Teichmuller曲线构造的Veech和沃德作为特殊情况。该构造本质上依赖于超几何微分算子的性质。对于小的m，我们找到了生成这些泰希-穆勒曲线的台球桌.我们解释了一些所谓的李雅普诺夫指数的Kontsevich-Zorich cocycle的正常化程度的一个自然的线丛的Teichmuller曲线。我们确定我们构造的Teichmuller曲线的李雅普诺夫指数。
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.