绞链多项式的一个性质及其在接触几何中的应用

编织模的有限性与全纯性

Finiteness and holonomicity of skein modules

本文通过引入边界，证明三维流形编织模的有限性，并利用编织转移双模和q-模拟方法，证明内部编织模的全纯性，包括有限生成与拉格朗日支撑条件。

Infinite families of hyperbolic $3$-manifolds with finite dimensional skein modules

The Kauffman bracket skein module $K(M)$ of a $3$-manifold $M$ is the quotient of the $\mathbb{Q}(A)$-vector space spanned by isotopy classes of links in $M$ by the Kauffman relations. A conjecture of Witten states that if $M$ is closed then $K(M)$ is finite dimensional. We introduce a version of this conjecture for manifolds with boundary and prove a stability property for generic Dehn-filling of knots. As a result we provide the first hyperbolic examples of the conjecture, proving that almost all Dehn-fillings of any two-bridge knot satisfies the conjecture.

来自接触同源性II的结和辫不变量，附与悉达多·加吉尔共同撰写的附录

Knot and braid invariants from contact homology II, with an appendix written jointly with Siddhartha Gadgil

我们提出了一个拓扑解释结和辫子接触同源度为零，在绳索和绞关系。这种解释使我们能够扩展结不变嵌入图和高维结。我们计算两桥结的结不变量，并将其与一般结的双分支覆盖联系起来。在附录中，我们证明了绳环是由纽结的基本群和外围结构决定的，并给出了应用。

On the S^1 x S^2 HOMFLY-PT invariant and Legendrian links

In \cite{GZ}, Gilmer and Zhong established the existence of an invariant for links in $S^1\times S^2$ which is a rational function in variables $a$ and $s$ and satisfies the HOMFLY-PT skein relations. We give formulas for evaluating this invariant in terms of a standard, geometrically simple basis for the HOMFLY-PT skein module of the solid torus. This allows computation of the invariant for arbitrary links in $S^1\times S^2$ and shows that the invariant is in fact a Laurent polynomial in $a$ and $z= s -s^{-1}$. Our proof uses connections between HOMFLY-PT skein modules and invariants of Legen…

联系Dehn外科、辛填充物和Property P以获得打结

Contact Dehn surgery, symplectic fillings, and Property P for knots

这是2005年在波恩举行的数学工作会议上的一个演讲的笔记。根据Ozbagci-Stipsicz的思想，给出了切触3-流形上Eliashberg凹填充定理的一个基于切触Dehn手术的证明.该定理在Kronheimer-Mrowka证明非平凡结的性质P中的作用被勾勒出来。

Examples of planar tight contact structures with support norm one

We exhibit an infinite family of tight contact structures with the property that none of the supporting open books minimizes the genus and maximizes the Euler characteristic of the page simultaneously, answering a question of Baldwin and Etnyre in arXiv:0910.5021 .