AN INTRODUCTION TO KNOT FLOER HOMOLOGY
AN INTRODUCTION TO KNOT FLOER HOMOLOGY
复制标题
结花同源性简介
DOI：
10.1090/conm/680/13701
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Ciprian Manolescu
中科院分区：
文献类型：
--
作者：
Ciprian Manolescu
这是一篇关于纽结弗洛尔同调的综述文章。我们提出了三种结构的不变量：原来的一个使用全纯磁盘，组合描述使用网格diagrams，和组合描述的立方分辨率。我们讨论的几何信息所携带的结弗洛尔同源，和连接到三维和四维拓扑通过手术公式。我们还描述了与Khovanov-Rozansky同调的一些拓扑关系。纽结弗洛尔同调是三流形中纽结和链环的不变量。它由Ozsvath-Szabo（OS 04 c）和Rasmussen（Ras 03）在2002年左右独立推出。从那时起，它已经发展成为一个大问题。其重要性在于，它包含了关于结的几个非平凡几何属性（属、切片属、纤维性、手术效果等）的信息。此外，纽结弗洛尔同调是可计算的：存在可以计算任意纽结的通用算法。这些算法往往会随着节点复杂性的增加而变慢，但也有不同的方法可以应用于特殊类别的节点，并给出显式的
This is a survey article about knot Floer homology. We present three constructions of this invariant: the original one using holomorphic disks, a combinatorial description using grid dia- grams, and a combinatorial description in terms of the cube of resolutions. We discuss the geomet- ric information carried by knot Floer homology, and the connection to three- and four-dimensional topology via surgery formulas. We also describe some conjectural relations to Khovanov-Rozansky homology. Knot Floer homology is an invariant of knots and links in three-manifolds. It was introduced independently by Ozsvath-Szabo (OS04c) and Rasmussen (Ras03) around 2002. Since then it has grown into a large subject. Its importance lies in the fact that it contains information about several non-trivial geometric properties of the knot (genus, slice genus, fiberedness, effects of surgery, etc.) Furthermore, knot Floer homology is computable: There exist general algorithms that can calculate it for arbitrary knots. These algorithms tend to get slow as the complexity of the knot increases, but there are also different methods that can be applied to special classes of knots and give explicit