Knots in Washington XVIII: Khovanov homology

摘要奖：DMS-0432284主要研究者：Jozef H. Przytycki该奖项为该系列的第18次会议“华盛顿的结”提供了部分参与者支持。这次会议的主题是霍瓦诺夫同调，目的是把新理论的指数与最近和当前的学生在拓扑学，沿着经验丰富的研究人员在其他方面的纽结理论和量子拓扑学。大量的方法已经开发出计算数字或多项式，每一个措施的一些方面的复杂性的一个knotted曲线在空间。 亚历山大多项式，这是大约70岁，是第一个例子，这类强大的工具。 大约20年前，随着琼斯多项式和相关不变量的发现，寻找更清晰的方法来区分一个纽结和另一个纽结，并理解相关的几何问题的速度加快了。 1999年，加州大学戴维斯分校的Mikhail Khovanov发现，琼斯多项式可以被看作是一个丰富理论的一行总结，正在进行的关于Khovanov思想的工作将是这次会议的主题。

AbstractAward: DMS-0432284Principal Investigator: Jozef H. PrzytyckiThis award provides partial participant support for the 18thconference in the series, "Knots in Washington." This meeting isdevoted to the theme of Khovanov homology, and aims to bringexponents of that new theory together with recent and currentstudents in topology, along with experienced researchers in otheraspects of knot theory and quantum topology.A large number of methods have been developed for computingnumbers or polynomials that each measure some aspect of thecomplexity of a knotted curve in space. The Alexanderpolynomial, which is approximately 70 years old, is the firstexample of this powerful class of tools. The search forsharper ways to distinguish one knot from another and tounderstand associated geometric questions gathered speedapproximately 20 years ago with the discovery of the Jonespolynomial and related invariants. Mikhail Khovanov of theUniversity of California, Davis, found in 1999 that the Jonespolynomial can be viewed as a one-line summary of a richertheory, and ongoing work with Khovanov's ideas will be thetheme of this conference.