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Caroline Series

Non-singularity of bending lengths near convex structures.

Abstract: Suppose that N is a geometrically finite hyperbolic 3-manifold with boundary, such that the bending locus of the boundary of its convex core is a collection of simple closed curves a_1,..., a_n. We give topological conditions on the a_i for such a convex structure to exist, and prove that the map which associates to each structure the hyperbolic lengths of the curves a_i is a global diffeomorphism from the set of all convex structures bent along a_1,..., a_n onto its image. If the set of curves is maximal, their traces (or complex lengths) are local parameters for the representation space R(N).