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arXiv:1408.1630 [math.AG]AbstractReferencesReviewsResources

Eigenvalues of Curvature, Lyapunov exponents and Harder-Narasimhan filtrations

Fei Yu

Published 2014-08-07, updated 2014-10-22Version 2

Inspired by Katz-Mazur theorem on crystalline cohomology, also base on Eskin-Kontsevich-Zorich's numerical experiments, we conjecture that the polygon of Lyapunov spectrum lies above (or on) the Harder-Narasimhan polygon on Teichmuller curves. The conjecture is verified for almost all Teichmuller curves in low genus strata. We also discuss the connections between them and the integral of eigenvalues of the Hodge bundle curvature by using Atiyah-Bott, Forni and Moller's works.

Comments: 31 pages. A new observation appeared in Remark 5.11. Update some references. arXiv admin note: text overlap with arXiv:1112.5872, arXiv:1204.1707 by other authors
Subjects: 32G15, 30F60, 14H10, 37D25, 53C07
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