TQFT for General Lie Algebras and Applications to Open 3-Manifolds

We review Kohno's definition of 3-manifold invariants coming from the conformal field theory associated to a simple Lie algebra $g$ (and a level $k$) and extend it to a topological quantum field theory in dimension 3. As an application, some invariants at infinity of open 3-manifolds, derived from the TQFT, are considered. Explicit computations, using mapping class group representations, are performed for a series of Whitehead manifolds. An example of an uncountable family of pairwise non-homeomorphic contractible open 3-manifolds is given