Are there p-adic knot invariants?

Abstract

We suggest to use the Hall-Littlewood version of Rosso-Jones formula to define the germs of $p$-adic HOMFLY-PT polynomials for torus knots $[m,n]$, which possess at least the $[m,n]⟷[n,m]$ topological invariance. This calls for generalizations to other knot families and is a challenge for several branches of modern theory.

4 pages

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Cited by in corpus (15)

• $p$-Adic Mathematical Physics: The First 30 Years
• Differential expansion and rectangular HOMFLY for the figure eight knot
• HOMFLY polynomials in representation [3,1] for 3-strand braids
• On rectangular HOMFLY for twist knots
• Nimble evolution for pretzel Khovanov polynomials
• Are Khovanov-Rozansky polynomials consistent with evolution in the space of knots?
• On moduli space of symmetric orthogonal matrices and exclusive Racah matrix $\bar{S}$ for representation $R=[3,1]$ with multiplicities
• Rectangular superpolynomials for the figure-eight knot
• Perspectives of differential expansion
• Extension of KNTZ trick to non-rectangular representations
• Knot polynomials for twist satellites
• On exclusive Racah matrices $\bar{S}$ for rectangular representations
• HOMFLY for twist knots and exclusive Racah matrices in representation [333]
• Pentad and triangular structures behind the Racah matrices
• Defect and degree of the Alexander polynomial