Eigenvalues of curvature, Lyapunov exponents and Harder–Narasimhan filtrations

Yu, Fei

doi:10.2140/gt.2018.22.2253

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Eigenvalues of curvature, Lyapunov exponents and Harder–Narasimhan filtrations

Fei Yu

Geometry & Topology 22 (2018) 2253–2298

DOI: 10.2140/gt.2018.22.2253

Abstract

Inspired by the Katz–Mazur theorem on crystalline cohomology and by the numerical experiments of Eskin, Kontsevich and Zorich, we conjecture that the polygon of the Lyapunov spectrum lies above (or on) the Harder–Narasimhan polygon of the Hodge bundle over any Teichmüller curve. We also discuss the connections between the two polygons and the integral of eigenvalues of the curvature of the Hodge bundle by using the works of Atiyah and Bott, Forni, and Möller. We obtain several applications to Teichmüller dynamics conditional on the conjecture.

Keywords

moduli space of Riemann surface, Teichmüller geodesic flow, eigenvalue of curvature, Lyapunov exponent, Harder–Narasimhan filtration

Mathematical Subject Classification 2010

Primary: 14H10, 30F60, 32G15

Secondary: 37D25, 53C07

References

Publication

Received: 12 October 2016

Accepted: 21 August 2017

Published: 5 April 2018

Proposed: Benson Farb

Seconded: Dan Abramovich, Dmitri Burago

Authors

Fei Yu
School of Mathematical Sciences Zhejiang University Hangzhou China
http://www.math.zju.edu.cn/teacherintroen.asp?userid=330

Volume 22, issue 4 (2018)