Eigenvalues of Curvature, Lyapunov exponents and Harder-Narasimhan filtrations
Eigenvalues of Curvature, Lyapunov exponents and Harder-Narasimhan filtrations
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DOI：
10.2140/gt.2018.22.2253
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发表时间：
2014-08
期刊：
影响因子：
--
通讯作者：
Fei Yu
中科院分区：
文献类型：
--
作者：
Fei Yu
受晶体上同调的Katz-Mazur定理和Ekin-Kontsevich-Zorich的数值实验的启发，我们猜想Lyapunov谱的多边形位于任意Teichm-uller曲线上的Hodge丛的Harder-Narasimhan多边形上方(或之上)，并利用Atiyah-Bott，Forni和M\Oler的工作讨论了这两个多边形之间的联系和Hodge丛曲率的本征值积分.在满足这个猜想的条件下，我们得到了Teichm“Uller动力学的几个应用。
Inspired by Katz-Mazur theorem on crystalline cohomology and by Eskin-Kontsevich-Zorich's numerical experiments, we conjecture that the polygon of Lyapunov spectrum lies above (or on) the Harder-Narasimhan polygon of the Hodge bundle over any Teichm\"uller curve. We also discuss the connections between the two polygons and the integral of eigenvalues of the curvature of the Hodge bundle by using Atiyah-Bott, Forni and M\"oller's works. We obtain several applications to Teichm\"uller dynamics conditional to the conjecture.