an:07299385
Zbl 07299385
Bishler, L.; Dhara, Saswati; Grigoryev, T.; Mironov, A.; Morozov, A.; Morozov, An.; Ramadevi, P.; Singh, Vivek Kumar; Sleptsov, A.
Distinguishing mutant knots
EN
J. Geom. Phys. 159, Article ID 103928, 31 p. (2021).
00457327
2021
j
57K10 57K16 57K14
Chern-Simons theory; knot theory; mutant knots; HOMFLY-PT polynomials
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.