Total curvatures of holonomic links

q-holonomic formulas for colored HOMFLY polynomials of 2-bridge links

We compute q-holonomic formulas for the HOMFLY polynomials of 2-bridge links colored with one-column (or one-row) Young diagrams.

源自带状态Skein代数的量子和乐链接不变量

Quantum holonomic link invariants derived from stated skein algebras

本文基于带状态skein代数表示理论为标架链环定义了不变量，推导了其规范不变性，揭示了与量子群及量子双曲几何构造的联系，并给出了R矩阵显式公式以计算不变量。

The colored HOMFLY polynomial is q-holonomic

We prove that the colored HOMFLY polynomial of a link, colored by symmetric or exterior powers of the fundamental representation, is q-holonomic with respect to the color parameters. As a result, we obtain the existence of an (a,q) super-polynomial of all knots in 3-space. Our result has implications on the quantization of the SL(2,C) character variety of knots using ideal triangulations or the topological recursion, and motivates questions on the web approach to representation theory.

Local Structure of Ideal Shapes of Knots, II, Constant Curvature Case

The thickness, NIR(K) of a knot or link K is defined to be the radius of the largest solid tube one can put around the curve without any self intersections, which is also known as the normal injectivity radius of K. For C^{1,1} curves K, NIR(K)=min{(1/2)DCSC(K),(1/(supkappa(K))))}, where kappa(K) is the generalized curvature, and the double critical self distance DCSD(K) is the shortest length of the segments perpendicular to K at both end points. The knots and links in ideal shapes (or tight knots or links) belong to the minima of ropelength = length/thickness within a fixed isotopy class. In…

谱序列配边上具有正数量曲率的度量族

Families of metrics with positive scalar curvature on spectral sequence cobordisms

本文研究Bloom单极Floer谱序列配边上的度量族，构造了满足指定渐近行为、具有正数量曲率的度量族，证明其可使谱序列计算仅需计数可约解，覆盖$T(2,n)$环面纽结等构型类别。

Knots of Constant Curvature

In this paper we show how to realize all knot (and link) types as C^{2} smooth curves of constant curvature. Our proof is constructive: we build the knots with copies of a fixed finite number of "building blocks" that are particular segments of helices and circles. We use these building blocks to construct all closed braids.