Title: The Kontsevich integral for bottom tangles in handlebodies,
Abstract: The Kontsevich integral is a powerful link invariant, taking values in spaces
of Jacobi diagrams. In this paper, we extend the Kontsevich integral to
construct a functor on the category of bottom tangles in handlebodies. This
functor gives a universal finite type invariant of bottom tangles, and refines
a functorial version of the Le-Murakami-Ohtsuki 3-manifold invariant for
Lagrangian cobordisms of surfaces.