We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Evolution for Khovanov polynomials for figure-eight-like family of knots.
- Authors
Dunin-Barkowski, Petr; Popolitov, Aleksandr; Popolitova, Svetlana
- Abstract
We look at how evolution method deforms, when one considers Khovanov polynomials instead of Jones polynomials. We do this for the figure-eight-like knots (also known as 'double braid' knots, see arXiv:1306.3197) — a two-parametric family of knots which "grows" from the figure-eight knot and contains both two-strand torus knots and twist knots. We prove that parameter space splits into four chambers, each with its own evolution, and two isolated points. Remarkably, the evolution in the Khovanov case features an extra eigenvalue, which drops out in the Jones (t → − 1) limit.
- Subjects
POLYNOMIALS; CHERN-Simons gauge theory; BRAID group (Knot theory); KNOT theory; TORUS; EIGENVALUES
- Publication
International Journal of Modern Physics A: Particles & Fields; Gravitation; Cosmology; Nuclear Physics, 2022, Vol 37, Issue 36, p1
- ISSN
0217-751X
- Publication type
Article
- DOI
10.1142/S0217751X22502165