Categorification of the Colored Jones Polynomial and Rasmussen Invariant of Links
Categorification of the Colored Jones Polynomial and Rasmussen Invariant of Links
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有色琼斯多项式和拉斯穆森链接不变量的分类
DOI：
10.4153/cjm-2008-053-1
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
S. Wehrli
中科院分区：
文献类型：
--
作者：
A. Beliakova;S. Wehrli
我们定义了一个依赖于两个参数的彩色连杆的形式Khovanov括号族。这些括号的同构类是带框彩色链接的不变量。应用于这些括号的Bar-Natan函子产生了对有色琼斯多项式进行分类的Khovanov和Lee同调理论。进一步，我们研究了在何种条件下框架的彩色连杆协体在我们的形式括号之间引起链变换。我们推测，对于特殊的参数选择，彩色连杆的Khovanov和Lee同调理论是泛函的（直到符号）。最后，我们将Rasmussen不变量扩展到链接，并给出了这个不变量比多变量Levine-Tristram签名更强的阻碍剪切的例子。
Abstract We define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further, we study conditions under which framed colored link cobordisms induce chain transformations between our formal brackets. We conjecture that for special choice of parameters, Khovanov and Lee homology theories of colored links are functorial (up to sign). Finally, we extend the Rasmussen invariant to links and give examples where this invariant is a stronger obstruction to sliceness than the multivariable Levine–Tristram signature.