# Lower bounds for Lyapunov exponents of flat bundles on curves

@article{Eskin2016LowerBF, title={Lower bounds for Lyapunov exponents of flat bundles on curves}, author={A. V. Eskin and Maxim Kontsevich and Martin Moeller and Anton Zorich}, journal={arXiv: Geometric Topology}, year={2016} }

Consider a flat bundle over a complex curve. We prove a conjecture of Fei Yu that the sum of the top k Lyapunov exponents of the flat bundle is always greater or equal to the degree of any rank k holomorphic subbundle. We generalize the original context from Teichmueller curves to any local system over a curve with non-expanding cusp monodromies. As an application we obtain the large genus limits of individual Lyapunov exponents in hyperelliptic strata of Abelian differentials.
Understanding…

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## 19 Citations

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