The modified Family B detection conjecture

Let Km(t)K_m'(t) be the modified family of virtual knot diagrams illustrated in the paper. Let KN\langle K\rangle_N denote the NN-strand bracket polynomial. The modified Family B conjecture. Km(t)K_m'(t) is a non-classical virtual knot diagram and is not detected by the fundamental group or the NN-strand bracket polynomial unless N3N\geq 3. The claim concerns the modified family introduced after the analysis of Family B; its status is unresolved in the supplied text.

Sources & referencesView supporting material

Primary source

H. A. Dye, “Virtual knots undetected by 1 and 2-strand bracket polynomials”, arXiv:math/0402308 (2004).

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