Evolution properties of the knot's defect

Abstract

The defect of differential (cyclotomic) expansion for colored HOMFLY-PT polynomials is conjectured to be invariant under any antiparallel evolution and change linearly with the evolution in any parallel direction. In other words, each $\mathcal{R}$-matrix can be substituted by an entire 2-strand braid in two different ways: the defect remains intact when the braid is antiparallel and changes by half of the added length when the braid is parallel.

References in corpus (15)

• HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
• Character expansion for HOMFLY polynomials. III. All 3-Strand braids in the first symmetric representation
• Eigenvalue hypothesis for Racah matrices and HOMFLY polynomials for 3-strand knots in any symmetric and antisymmetric representations
• A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres
• On colored HOMFLY polynomials for twist knots
• An analytic version of the Melvin-Morton-Rozansky Conjecture
• On rectangular HOMFLY for twist knots
• Differential expansion for link polynomials
• Extension of KNTZ trick to non-rectangular representations
• On exclusive Racah matrices $\bar{S}$ for rectangular representations
• Mutant knots with symmetry
• Colored HOMFLY-PT polynomials of quasi-alternating $3$-braid knots
• Difference of mutant knot invariants and their differential expansion
• Cyclotomic expansions for the colored HOMFLY-PT invariants of double twist knots
• The colored HOMFLY-PT polynomials of the trefoil knot, the figure-eight knot and twist knots

Cited by in corpus (3)

• Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed
• Towards the theory of Yangians
• Defect and degree of the Alexander polynomial