F. Bonahon, Shearing hyperbolic surfaces, bending pleated surfaces, and Thurston's symplectic form, Ann. Fac. Sci. Toulouse 5 (1996), 233--297.  Home/Search   Document Not in Database   Summary   Related Articles

....the surface. More precisely, if we fix a maximal geodesic lamination #, the shearing coordinates for Teichm uller space identify T (S) to an open convex cone in the finite dimensional vector space H(#) of all transverse cocycles for #. These shearing coordinates were introduced and developed in [Bo1], but they already appear in dual form in [Th] This embedding of T (S) in H(#) identifies each tangent space T#T (S) to the vector space H(#) The main motivation for these shearing coordinates is that they are well adapted to the geodesic lamination #, and consequently provide useful tools for ....

....formula [Wo2] expressing the Weil Petersson form in these Fenchel Nielsen coordinates. Another special case is that of transverse cocycles which are transverse measures for the geodesic lamination. Because the Thurston intersection form puts in duality shearing coordinates and length functions [Bo1], the restriction of Theorem 1 to this case is just Wolpert s result [Wo2] that the Weil Petersson form establishes a duality between earthquakes vector fields and length functions. However, Theorem 1 is much more general since # admits many fewer transverse measures than transverse cocycles. The ....

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F. Bonahon, Shearing hyperbolic surfaces, bending pleated surfaces, and Thurston's symplectic form, Ann. Fac. Sci. Toulouse 5 (1996), 233--297.

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