Three-manifold invariants from Chern-Simons field theory with arbitrary semi-simple gauge groups

Invariants for framed links in S-3 obtained from Chern-Simons gauge field t heory based on an arbitrary gauge group (semi-simple) have been used to con struct a three-manifold invariant. This is a generalization of a similar co nstruction developed earlier for SU(2) Chern-Simons theory. The procedure e xploits a theorem of Lickorish and Wallace and also those of Kirby, Fenn an d Rourke which relate three-manifolds to surgeries on framed unoriented lin ks. The invariant is: an appropriate linear combination of framed link inva riants which does not change under Kirby calculus. This combination does no t see the relative orientation of the component knots. The invariant Is rel ated to the partition function of Chern-Simons theory. This thus provides a n efficient method of evaluating the partition function for these field the ories. As some examples, explicit computations of these manifold invariants : for a few three-manifolds have been done.