The Weil-Petersson and Thurston symplectic forms

DOI10.1215/S0012-7094-01-10836-3zbMath1014.32009OpenAlexW2055741698MaRDI QIDQ1847849

Francis Bonahon, Yaşar Sözen

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-01-10836-3

zbMATH Keywords

Teichmüller spaceWeil-Petersson formThurston's intersection form

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Foliations in differential topology; geometric theory (57R30) Symplectic structures of moduli spaces (53D30)

Related Items (19)

Cross ratios and identities for higher Teichmüller-Thurston theory ⋮ Cataclysms for Anosov representations ⋮ A symplectic map between hyperbolic and complex Teichmüller theory ⋮ Counting hyperbolic multigeodesics with respect to the lengths of individual components and asymptotics of Weil-Petersson volumes ⋮ Hamiltonian flows for pseudo-Anosov mapping classes ⋮ Length functions in Teichmüller and anti-de Sitter geometry ⋮ Valuations on the character variety: Newton polytopes and residual Poisson bracket ⋮ A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces ⋮ Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces ⋮ Quantum hyperbolic geometry ⋮ Representations of the quantum Teichmüller space and invariants of surface diffeomorphisms ⋮ Geodesic currents and counting problems ⋮ Projective structures, grafting and measured laminations ⋮ Reidemeister torsion of a symplectic complex ⋮ Shearing deformations of Hitchin representations and the Atiyah-Bott-Goldman symplectic form ⋮ Products of twists, geodesic lengths and Thurston shears ⋮ On normalizations of Thurston measure on the space of measured laminations ⋮ Counting mapping class group orbits under shearing coordinates ⋮ Kontsevich-Witten model from \(2+1\) gravity: new exact combinatorial solution

Cites Work

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• The symplectic nature of fundamental groups of surfaces
• Weil-Petersson volumes
• Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form
• Variations of the boundary geometry of \(3\)-dimensional hyperbolic convex cores
• Transverse Hölder distributions for geodesic laminations
• On discrete subgroups of Lie groups. I, II
• Some remarks on Teichmüller's space of Riemann surfaces
• Remarks on the cohomology of groups
• On the Weil-Petersson Geometry of the Moduli Space of Curves
• Combinatorics of Train Tracks. (AM-125)
• The Weil-Petersson Symplectic Structure at Thurston's Boundary
• On the Classical Transcendents of Mathematical Physics

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