Volume 22, issue 4 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 5, 2511–3144
Issue 4, 1893–2510
Issue 3, 1267–1891
Issue 2, 645–1266
Issue 1, 1–644

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Eigenvalues of curvature, Lyapunov exponents and Harder–Narasimhan filtrations

Fei Yu

Geometry & Topology 22 (2018) 2253–2298
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