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Distinguishing mutant knots. (English) Zbl 1458.57002

Summary: Knot theory is actively studied both by physicists and mathematicians as it provides a connecting centerpiece for many physical and mathematical theories. One of the challenging problems in knot theory is distinguishing mutant knots. Mutant knots are not distinguished by colored HOMFLY-PT polynomials for knots colored by either symmetric and or antisymmetric representations of \(SU(N)\). Some of the mutant knots can be distinguished by the simplest non-symmetric representation \([2,1 ]\). However there is a class of mutant knots which require more complex representations like \([4,2]\). In this paper we calculate polynomials and differences for the mutant knot polynomials in representations \([3,1]\) and \([4,2]\) and study their properties.

MSC:

57K10 Knot theory
57K16 Finite-type and quantum invariants, topological quantum field theories (TQFT)
57K14 Knot polynomials
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