TQFT for general Lie algebras and applications to open 3-manifolds. (English) Zbl 0881.57007

The author constructs a topological quantum field theory (TQFT) in dimension three from the 3-manifold invariants coming from the conformal field theory associated to a simple Lie algebra due to T. Kohno in [Topology 31, No. 2, 203-230 (1992; Zbl 0762.57011) and Contemp. Math. 175, 193-217 (1994; Zbl 0823.57004)].
By regarding an open manifold as an infinite composition of cobordisms, the TQFT associates an inverse system of vector spaces whose limit is a topological invariant. Explicit computations are performed to study contractible open 3-manifolds which are not homeomorphic to Euclidean 3-space.
Reviewer: J.Hebda (St.Louis)


57M25 Knots and links in the \(3\)-sphere (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)
57M30 Wild embeddings
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations