We show that any of the new knot invariants obtained from Chern-Simons theory
based on an arbitrary non-abelian gauge group do not distinguish isotopically
inequivalent mutant knots and links. In an attempt to distinguish these knots
and links, we study Murakami (symmetrized version) r-strand composite braids.
Salient features of the theory of such composite braids are presented.
Representations of generators for these braids are obtained by exploiting
properties of Hilbert spaces associated with the correlators of Wess-Zumino
conformal field theories. The r-composite invariants for the knots are given
by the sum of elementary Chern-Simons invariants associated with the
irreducible representations in the product of r representations (allowed by
the fusion rules of the corresponding Wess-Zumino conformal field theory)
placed on the r individual strands of the composite braid. On the other hand,
composite invariants for links are given by a weighted sum of elementary
multicoloured Chern-Simons invariants. Some mutant links can be distinguished
through the composite invariants, but mutant knots do not share this property.
The results, though developed in detail within the framework of SU(2)
Chern-Simons theory are valid for any other non-abelian gauge group.Comment: Latex, 25pages + 16 diagrams available on reques
