GEODESIC LAMINATIONS WITH TRANSVERSE HOLDER DISTRIBUTIONS

To interpolate between isotopy classes of simple closed curves on a su rface S, Thurston introduced the space ML(S) of geodesic laminations w ith transverse measures on S. The main purpose of this paper is to dev elop a differential calculus on ML(S). This space is a piecewise linea r manifold, but does not admit any natural differentiable structure. W e give an analytic interpretation of the combinatorial tangent vectors to ML(S), as geodesic laminations with a certain type of transverse d istributions. As an illustration, we apply this technique to determine the derivative of the length function associated to a hyperbolic 3-ma nifold.