虚拟辫子

Braiding Knots in Contact 3-Manifolds

We show that a transverse link in a contact structure supported by an open book decomposition can be transversely braided. We also generalize Markov's theorem on when the closures of two braids represent (transversely) isotopic links.

带有理开书分解的横截辫化定理

A Transverse Braiding Theorem with Rational Open Book Decomposition

本研究推广Pavelescu的论证，证明紧接触3-流形中任意横截链环都可相对于有理开书分解横截同痕为辫，推进了横截链环与有理开书分解相关的几何拓扑研究。

相互编织与辫群的带状表示

Mutual braiding and the band presentation of braid groups

本文研究了封闭辫与其轴线在鲁道夫意义下的“互辫”。它涉及封闭的辫子是不结的链接，最简单的情况是封闭的辫子，目前的unknot。相互编织的几何条件指的是存在一个密切的控制方式，其中整个家庭的纤维表面满足家庭的盘跨越编织轴。我们展示了如何这样的辫子可以自然地呈现为一个词的“带发电机”的辫子群讨论的伯曼，高和李在他们最近的帐户带介绍的辫群。在这种情况下，我们能够相互编织的条件转换成存在一个合适的序列的带关系和其他移动的辫子字，并得出一个组合的方法来决定是否辫子是相互编织。

Holonomy braidings, biquandles and quantum invariants of links with $SL_2(\mathbb C)$ flat connections

R. Kashaev and N. Reshetikhin introduced the notion of holonomy braiding extending V. Turaev's homotopy braiding to describe the behavior of cyclic representations of the unrestricted quantum group $U_qsl_2$ at root of unity. In this paper, using quandles and biquandles we develop a general theory for Reshetikhin-Turaev ribbon type functor for tangles with quandle representations. This theory applies to the unrestricted quantum group $U_qsl_2$ and produces an invariant of links with a gauge class of quandle representations.

Braiding link cobordisms and non-ribbon surfaces

We define the notion of a braided link cobordism in $S^3 \times [0,1]$, which generalizes Viro's closed surface braids in $\mathbb{R}^4$. We prove that any properly embedded oriented surface $W \subset S^3 \times [0,1]$ is isotopic to a surface in this special position, and that the isotopy can be taken rel boundary when $\partial W$ already consists of closed braids. These surfaces are closely related to another notion of surface braiding in $D^2 \times D^2$, called braided surfaces with caps, which are a generalization of Rudolph's braided surfaces. We mention several applications of braided…

Braiding surface links which are coverings over the standard torus

We consider a surface link in the 4-space which can be presented by a simple branched covering over the standard torus, which we call a torus-covering link. Torus-covering links include spun $T^2$-knots and turned spun $T^2$-knots. In this paper we braid a torus-covering link over the standard 2-sphere. This gives an upper estimate of the braid index of a torus-covering link. In particular we show that the turned spun $T^2$-knot of the torus $(2,\,p)$-knot has the braid index four.