Mutant knots with symmetry

Abstract

Mutant knots, in the sense of Conway, are known to share the same Homfly polynomial. Their 2-string satellites also share the same Homfly polynomial, but in general their m-string satellites can have different Homfly polynomials for m>2. We show that, under conditions of extra symmetry on the constituent 2-tangles, the directed m-string satellites of mutants share the same Homfly polynomial for m<6 in general, and for all choices of m when the satellite is based on a cable knot pattern. We give examples of mutants with extra symmetry whose Homfly polynomials of some 6-string satellites are different, by comparing their quantum sl(3) invariants.

15 pages

References in corpus (1)

• Geometrical relations and plethysms in the Homfly skein of the annulus

Cited by in corpus (8)

• Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
• Tabulating knot polynomials for arborescent knots
• Multiplicity-free $U_q(s{l}_N)$ 6-j symbols: relations, asymptotics, symmetries
• Distinguishing Mutant Knots
• Gaussian distribution of LMOV numbers
• Difference of mutant knot invariants and their differential expansion
• Evolution properties of the knot's defect
• Vogel's universality and the classification problem for Jacobi identities