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

J. Math. Sci. Univ. Tokyo
Vol. 4 (1997), No. 1, Page 121--181.

Funar, Louis
TQFT for General Lie Algebras and Applications to Open 3-Manifolds
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Abstract:
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.

Mathematics Subject Classification (1991): 57M25, 57N10, 57M30, 81Q30, 81R10
Mathematical Reviews Number: MR1451305