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- W4285160266 abstract "<p style='text-indent:20px;'>We consider the derivative <inline-formula><tex-math id=M1>begin{document}$ Dpi $end{document}</tex-math></inline-formula> of the projection <inline-formula><tex-math id=M2>begin{document}$ pi $end{document}</tex-math></inline-formula> from a stratum of Abelian or quadratic differentials to Teichmüller space. A closed one-form <inline-formula><tex-math id=M3>begin{document}$ eta $end{document}</tex-math></inline-formula> determines a relative cohomology class <inline-formula><tex-math id=M4>begin{document}$ [eta]_Sigma $end{document}</tex-math></inline-formula>, which is a tangent vector to the stratum. We give an integral formula for the pairing of <inline-formula><tex-math id=M5>begin{document}$ Dpi([eta]_Sigma) $end{document}</tex-math></inline-formula> with a cotangent vector to Teichmüller space (a quadratic differential). We derive from this a comparison between Hodge and Teichmüller norms, which has been used in the work of Arana-Herrera on effective dynamics of mapping class groups, and which may clarify the relationship between dynamical and geometric hyperbolicity results in Teichmüller theory.</p>" @default.
- W4285160266 created "2022-07-14" @default.
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- W4285160266 date "2022-01-01" @default.
- W4285160266 modified "2023-09-25" @default.
- W4285160266 title "Hodge and Teichmüller" @default.
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- W4285160266 doi "https://doi.org/10.3934/jmd.2022007" @default.
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