When the theories meet: Khovanov homology as Hochschild homology of links
When the theories meet: Khovanov homology as Hochschild homology of links
复制标题
当理论相遇时：霍瓦诺夫同源性作为链接的霍克希尔德同源性
DOI：
--
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
J. Przytycki
中科院分区：
文献类型：
--
作者：
J. Przytycki
我们发现，Khovanov同调和Hochschild同调理论有一个共同的结构。事实上，它们是重叠的：2; n/ torus链接的Khovanov同调可以被解释为强调Khovanov同调的代数的Hochschild同调。在经典的Khovanov同调的情况下，我们证明了具体的联系。在Khovanov-Rozansky sl.n/同调及其变形的一般情况下，我们猜想的连接。最好的框架来探索我们的想法是使用一个余乘法自由版本的Khovanov同调图开发的L。Helme-Guizon和Y. Rong和这里推广到M-约化的情况，并在多边形的情况下推广到非交换代数。在这个框架下，我们证明了对任何单位代数A的Hochschild同调同构于多边形A上的图上同调。我们希望，本文将鼓励流动的思想在两个方向之间的Hochschild/循环同源性和Khovanov同源性理论。
We show that Khovanov homology and Hochschild homology theories share a common structure. In fact they overlap: Khovanov homology of the .2; n/ torus link can be interpreted as a Hochschild homology of the algebra underlining the Khovanov homology. In the classical case of Khovanov homology we prove the concrete connection. In the general case of Khovanov-Rozansky sl.n/ homology and their deformations we conjecture the connection. The best framework to explore our ideas is to use a comultiplication-free version of Khovanov homology for graphs developed by L. Helme-Guizon and Y. Rong and extended here to the M-reduced case, and in the case of a polygon extended to noncommutative algebras. In this framework we prove that for any unital algebra A the Hochschild homology of A is isomorphic to graph cohomology over A of a polygon. We expect that this paper will encourage a flow of ideas in both directions between Hochschild/cyclic homology and Khovanov homology theories.