Lyapunov exponents of the Hodge bundle over strata of quadratic differentials with large number of poles

We show an upper bound for the sum of positive Lyapunov exponents of any Teichmüller curve in strata of quadratic differentials with at least one zero of large multiplicity. As a corollary, it holds for any $\mathrm{SL} (2, \mathbb{R})$-invariant submanifold defined over $\mathbb{Q}$ in these strata. This proves Grivaux–Hubert’s conjecture about the asymptotics of Lyapunov exponents for strata with a large number of poles in the situation when at least one zero has high multiplicity.

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Received 1 December 2016

Accepted 22 March 2018

Published 16 November 2018