相关论文: Torus Knots and the Chern-Simons path integral: a …

In this paper, the authors give an unknotting sequence for torus knots and also provide unknotting numbers of $_n14_{17191}, \ _n14_{14274}, \ _n14_{18351}, \ _n14_{24498}$ and some other knots from the knot table of Hoste-Thistlethwite.

We formulate a stability conjecture for the coefficients of the colored Jones polynomial of a knot, colored by irreducible representations in a fixed ray of a simple Lie algebra, and verify it for all torus knots and all simple Lie algebras…

Chern-Simons gauge theory for compact semisimple groups is analyzed from a perturbation theory point of view. The general form of the perturbative series expansion of a Wilson line is presented in terms of the Casimir operators of the gauge…

We observe that the strong slope conjecture implies that the degree of the colored Jones polynomial detects all torus knots. As an application we obtain that an adequate knot that has the same colored Jones polynomial degrees as a torus…

Polynomial invariants corresponding to the fundamental representation of the gauge group $SU(N)$ are computed for arbitrary torus knots and links in the framework of Chern-Simons gauge theory making use of knot operators. As a result, a…

We study the asymptotic behavior of the Witten-Reshetikhin-Turaev invariant associated with the square of the $n$-th root of unity with odd $n$ for a Seifert fibered space obtained by an integral Dehn surgery along a torus knot. We show…

This is the second of three papers that refine and extend portions of our earlier preprint, "The depth of a knot tunnel." Together, they rework the entire preprint. The theory of tunnel number 1 knots that we introduced in "The tree of knot…

A slice-torus invariant is an $\mathbb{R}$-valued homomorphism on the knot concordance group whose value gives a lower bound for the 4-genus such that the equality holds for any positive torus knot. Such invariants have been discovered in…

In 2003, Hikami and Kirillov uncovered an intriguing connection between torus knots $\mathcal{K}_{(P,Q)}$ and Virasoro minimal models $\mathcal{M}(P,Q)$ by relating the Kashaev invariants of the knots to the characters of the corresponding…

Motivated by an amazing integrality structure conjecture for the $U(N)$ Chern-Simons quantum invariants of framed knots investigated by Mari\~no and Vafa, a new conjectural formula, named Hecke lifting conjecture, was proposed in…

Torus knots are an important family of knots about which much is understood; invariants of torus knots often exhibit nice formulas, making them convenient and fundamental building blocks for examples in knot theory. Spiral knots, defined…

Region crossing change for a knot or a proper link is an unknotting operation. In this paper, we provide a sharp upper bound on the region unknotting number for a large class of torus knots and proper links. Also, we discuss conditions on…

We construct geometrically two universal link invariants: universal ADO invariant and universal Jones invariant, as limits of invariants given by graded intersections in configuration spaces. More specifically, for a fixed level $\mathscr…

The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-Simons theory, possess an especially simple representation for torus knots, which begins from quantum R-matrix and ends up with a trivially-looking split W…

We propose a conjecture to compute the all-order asymptotic expansion of the colored Jones polynomial of the complement of a hyperbolic knot, J_N(q = exp(2u/N)) when N goes to infinity. Our conjecture claims that the asymptotic expansion of…

We introduce the concept of tied links in the solid torus, which generalize naturally the concept of tied links in $S^3$ previously introduced by Aicardi and Juyumaya. We also define an invariant of these tied links by using skein…

We study the conjecture that a sum of the (g-1)st powers of adjoint Reidemeister torsions for a torus knot is an integer. We prove that the conjecture is true for any torus knot and all non-negative g. To prove the conjecture, we introduce…

The unknotting number of a knot is bounded from below by its slice genus. It is a well-known fact that the genera and unknotting numbers of torus knots coincide. In this note we characterize quasipositive knots for which the genus bound is…

We introduce a three variable series invariant $F_K (y,z,q)$ for plumbed knot complements associated with a Lie superalgebra $sl(2|1)$. The invariant is a generalization of the $sl(2|1)$-series invariant $\hat{Z}(q)$ for closed 3-manifolds…

We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions,…