Chirality of knots 9₄₂ and 10₇₁ and Chern-Simons theory

Abstract

Up to 10 crossing numbers, there are two knots, 9₄₂ and 10₇₁ whose chirality is not detected by any of the known polynomials, namely, Jones invariants and their two variable generalizations, HOMFLY and Kauffman invariants. We show that the generalized knot invariants, obtained through SU(2) Chern-Simons topological field theory, which give the known polynomials as special cases, are indeed sensitive to the chirality of these knots.