Title: Character Varieties and Hyperbolic 3-manifolds
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Abstract: The SL(2,C) character variety of a finite volume hyperbolic
3-manifold is a complex algebraic set, X(M).  This moduli space
encodes a great deal of topological data about M. The canonical
component of X(M) is a deformation space of M, as seen in Thurston's
hyperbolic Dehn surgery theorem. Character varieties have been key
ingredients in many aspects of modern topology, including the proof of
the cyclic surgery theorem.  They can also be used to detect essential
surfaces in manifolds and splittings of their fundamental groups.
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I will introduce this set and discuss the relationship between the
topology of M and the algebraic geometric structure of X(M). I will
focus on the case where M has one cusp, where the canonical component
of X(M) is a curve.