Abstract
To interpolate between isotopy classes of simple closed curves on a surface S , Thurston introduced the space ML(S) of geodesic laminations with transverse measures on S. The main purpose of this paper is to develop a differential calculus on ML(S) . This space is a piecewise linear manifold, but does not admit any natural differentiable structure. We give an analytic interpretation of the combinatorial tangent vectors to ML(S) , as geodesic laminations with a certain type of transverse distributions. As an illustration, we apply this technique to determine the derivative of the length function associated to a hyperbolic 3-manifold.
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