Bar-natan's geometric complex and Dye-Kauffman-Manturov's categorification
Bar-natan's geometric complex and Dye-Kauffman-Manturov's categorification
复制标题
Bar-natan 的几何复形和 Dye-Kauffman-Manturov 的分类
DOI：
10.1142/s0218216515500765
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Keiji Tagami
中科院分区：
文献类型：
--
作者：
A. Tsuji;S. Okano and M. Mochizuki;A. Tsuji;岡留 有哉;岡留 有哉;岡留 有哉;Keiji Tagami
在本文中，我们利用 Turaev 给出的 Bar-Natan 的 Khovanov 同源同伦量子场论 (HQFT) 构造，构造了二变量 Dye-Kauffman-Miyazawa 多项式的分类。特别是，对于任何稳定的等价类，我们构造一个分级链接同调性，其分级欧拉特征是二变量 Dye-Kauffman-Miyazawa 多项式。此外，我们证明它与 Dye-Kauffman-Manturov 分类的一个特例是同构的。从这个意义上说，我们用Bar-Natan的构造来解释Dye-Kauffman-Manturov同源性的特殊情况。
In this paper, we construct a categorification of the two-variable Dye–Kauffman–Miyazawa polynomial by utilizing Bar-Natan’s construction of the Khovanov homology and homotopy quantum field theories (HQFTs) given by Turaev. In particular, for any stable equivalence class, we construct a-graded link homology overwhose graded Euler characteristic is the two-variable Dye–Kauffman–Miyazawa polynomial. Moreover, we show that it is isomorphic to a special case of Dye–Kauffman–Manturov’s categorification. In this sense, we explain the special case of Dye–Kauffman–Manturov’s homology in terms of Bar-Natan’s construction.