arXiv:math/0508508 Abstract

arXiv:math/0508508 [math.DS]Abstract References Reviews Resources

Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture

Published 2005-08-25Version 1

We prove the Zorich-Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichm\"uller flow on (any connected component of a stratum of) the moduli space of Abelian differentials on compact Riemann surfaces are all distinct. By previous work of Zorich and Kontsevich, this implies the existence of the complete asymptotic Lagrangian flag describing the behavior in homology of the vertical foliation in a typical translation surface.

Comments: 36 pages

Categories: math.DS

Keywords: zorich-kontsevich conjecture, lyapunov spectra, simplicity, complete asymptotic lagrangian flag describing, compact riemann surfaces

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