Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-05-10
Commun.Math.Phys. 217 (2001) 295-314
Physics
High Energy Physics
High Energy Physics - Theory
24 pages Latex file, 26 eps files, included generalisations for arbitrary semi-simple group, corrected typos
Scientific paper
10.1007/s002200000347
Invariants for framed links in $S^3$ obtained from Chern-Simons gauge field theory based on an arbitrary gauge group (semi-simple) have been used to construct a three-manifold invariant. This is a generalization of a similar construction developed earlier for SU(2) Chern-Simons theory. The procedure exploits a theorem of Lickorish and Wallace and also those of Kirby, Fenn and Rourke which relate three-manifolds to surgeries on framed unoriented links. The invariant is an appropriate linear combination of framed link invariants which does not change under Kirby calculus. This combination does not see the relative orientation of the component knots. The invariant is related to the partition function of Chern-Simons theory. This thus provides an efficient method of evaluating the partition function for these field theories. As some examples, explicit computations of these manifold invariants for a few three-manifolds have been done.
Kaul Romesh K.
Ramadevi P.
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