Evolution properties of the knot's defect
arXiv:2204.05977 · doi:10.1140/epjc/s10052-022-10705-2
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 -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.
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