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

Kaul, Romesh K. ; Ramadevi, P. (2001) Three-manifold invariants from Chern-Simons field theory with arbitrary semi-simple gauge groups Communications in Mathematical Physics, 217 (2). pp. 295-314. ISSN 0010-3616

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Official URL: http://www.springerlink.com/content/eg6qpu5wm5epkq...

Related URL: http://dx.doi.org/10.1007/s002200000347

Abstract

Invariants for framed links in S3 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.

Item Type:Article
Source:Copyright of this article belongs to Springer-Verlag.
ID Code:16429
Deposited On:15 Nov 2010 13:40
Last Modified:06 Jun 2011 04:47

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