Duke Mathematical Journal

The Weil-Petersson and Thurston symplectic forms

Francis Bonahon and Yaşar Sözen

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We consider the Weil-Petersson form on the Teichmüller space $\mathscr {T}$(S) of a surface S of genus at least 2, and we compute it in terms of the shearing coordinates for $\mathscr {T}$(S) associated to a geodesic lamination λ on S. In the corresponding expression, the Weil-Petersson form coincides with Thurston's intersection form on the space of transverse cocycles for λ.

Article information

Duke Math. J., Volume 108, Number 3 (2001), 581-597.

First available in Project Euclid: 5 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Secondary: 53D30: Symplectic structures of moduli spaces 57R30: Foliations; geometric theory


Sözen, Yaşar; Bonahon, Francis. The Weil-Petersson and Thurston symplectic forms. Duke Math. J. 108 (2001), no. 3, 581--597. doi:10.1215/S0012-7094-01-10836-3. https://projecteuclid.org/euclid.dmj/1091737184

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