
Alexander and Jones-type properties of the Links–Gould polynomialMatthew Harper - Department of Mathematics, Michigan State University
Alexander and Jones-type properties of the Links–Gould polynomialMatthew Harper - Department of Mathematics, Michigan State University
The Links-Gould (LG) polynomials are two-variable link invariants arising from the quantum supergroup Uq(sl(2|1)), exhibiting hybrid behavior between the Jones and Alexander polynomials. I will give an overview their constriction from representation theory and the modified Reshetikhin-Turaev construction, then survey some recent results illustrating this theme.
The basic LG invariant provides a lower bound on the Seifert genus, and this extends to its colored versions. We provide a skein theoretic argument to show that it admits a specialization to the Akutsu-Deguchi-Ohstuki (ADO) invariant at a sixth root of unity. We discuss recent work that colored Links--Gould polynomials are not determined by colored Jones polynomials. Finally, we discuss the alternating coefficient property of LG on alternating knots, and an analogue of the Fox conjecture supported by computational evidence.
This is joint work, in various combinations, with Stavros Garoufalidis, Rinat Kashaev, Ben-Michael Kohli, Jiebo Song, Guillaume Tahar, and Emmanuel Wagner.
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