Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-01-15
Commun.Math.Phys. 209 (2000) 29-49
Physics
High Energy Physics
High Energy Physics - Theory
25 pages, 11 eps figures, harvmac file (big mode)
Scientific paper
10.1007/s002200050014
It is well known that any three-manifold can be obtained by surgery on a framed link in $S^3$. Lickorish gave an elementary proof for the existence of the three-manifold invariants of Witten using a framed link description of the manifold and the formalisation of the bracket polynomial as the Temperley-Lieb Algebra. Kaul determined three-manifold invariants from link polynomials in SU(2) Chern-Simons theory. Lickorish's formula for the invariant involves computation of bracket polynomials of several cables of the link. We describe an easier way of obtaining the bracket polynomial of a cable using representation theory of composite braiding in SU(2) Chern-Simons theory. We prove that the cabling corresponds to taking tensor products of fundamental representations of SU(2). This enables us to verify that the two apparently distinct three-manifold invariants are equivalent for a specific relation of the polynomial variables.
Naik Swatee
Ramadevi P.
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