Remarks on Definition of Khovanov Homology
Remarks on Definition of Khovanov Homology
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发表时间：
2002
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通讯作者：
M. Khovanov
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作者：
M. Khovanov
米哈伊尔Khovanov定义，图的一个有方向的经典链接，收集的群体编号对整数。这些基团被构建为某些链复合物的同源基团。这些复合体的欧拉特征是连杆的琼斯多项式的系数。这篇笔记的目的是用对拓扑学家更友好的术语重写这个构造。介绍了框架链的Khovanov同调的一个版本。对于其考夫曼括号涉及绞关系的框架链接，这些同调群由精确序列相关。
Mikhail Khovanov defined, for a diagram of an oriented classical link, a collection of groups numerated by pairs of integers. These groups were constructed as homology groups of certain chain complexes. The Euler characteristics of these complexes are coefficients of the Jones polynomial of the link. The goal of this note is to rewrite this construction in terms more friendly to topologists. A version of Khovanov homology for framed links is introduced. For framed links whose Kauffman brackets are involved in a skein relation, these homology groups are related by an exact sequence.