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Title: Hodge and Teichmüller

We consider the derivative \begin{document}$ D\pi $\end{document} of the projection \begin{document}$ \pi $\end{document} from a stratum of Abelian or quadratic differentials to Teichmüller space. A closed one-form \begin{document}$ \eta $\end{document} determines a relative cohomology class \begin{document}$ [\eta]_\Sigma $\end{document}, which is a tangent vector to the stratum. We give an integral formula for the pairing of \begin{document}$ D\pi([\eta]_\Sigma) $\end{document} 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.

 
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Award ID(s):
1856155
NSF-PAR ID:
10357980
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of Modern Dynamics
Volume:
18
Issue:
0
ISSN:
1930-5311
Page Range / eLocation ID:
149
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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