论文标题
在标准的基础上，三价顶点和接壤的结式同源
Trivalent vertices and bordered knot Floer homology in the standard basis
论文作者
论文摘要
我们在Ozsvath-Szabo的边界的Floer同源性的精神上定义了新的代数，本地双模型和Bimodule图。我们为它们配备了U_Q（gl（1 | 1））的2个占2个代表的结构，分别为1个词，分别为1个典型，并表明它们对U_Q的表示形式进行分类（GL（1 | 1）^ - ）以及它们之间的地图。与Ozsvath-Szabo的代数不同，这里考虑的代数可以是由Rouquier和作者最近引入的较高张量产品操作来建立的。 我们的双模型都是由Heegaard图中的全态磁盘计数的动机。对于正交叉和负横梁，双模模也可以表示为涉及奇异双模块和身份双模块的映射锥。实际上，它们源于soergel双模型通过rouquier complex的一种动作，以通常的方式，第一次（据作者所知）（据作者所知），在Heegaard Floer同源性中获得了编织双模型。 此外，奇异的交叉双模块自然地将两个双模型用于三价顶点。这种双模型尚未出现在以前的边界浮动方法中，用于打结浮子同源性。 SOERGEL类别的作用来自分类量子GL（2）对2个代理2类别的作用，与偏斜的二元性的思想相一致，其中三价顶点双模式与1个型号e相关联，f在分类量子中（2）。
We define new algebras, local bimodules, and bimodule maps in the spirit of Ozsvath-Szabo's bordered knot Floer homology. We equip them with the structure of 2-representations of the categorified negative half U^- of U_q(gl(1|1)), 1-morphisms of such, and 2-morphisms respectively, and show that they categorify representations of U_q(gl(1|1)^-) and maps between them. Unlike with Ozsvath-Szabo's algebras, the algebras considered here can be built from a higher tensor product operation recently introduced by Rouquier and the author. Our bimodules are all motivated by holomorphic disk counts in Heegaard diagrams; for positive and negative crossings, the bimodules can also be expressed as mapping cones involving a singular-crossing bimodule and the identity bimodule. In fact, they arise from an action of the monoidal category of Soergel bimodules via Rouquier complexes in the usual way, the first time (to the author's knowledge) such an expression has been obtained for braiding bimodules in Heegaard Floer homology. Furthermore, the singular crossing bimodule naturally factors into two bimodules for trivalent vertices; such bimodules have not appeared in previous bordered-Floer approaches to knot Floer homology. The action of the Soergel category comes from an action of categorified quantum gl(2) on the 2-representation 2-category of U^- in line with the ideas of skew Howe duality, where the trivalent vertex bimodules are associated to 1-morphisms E, F in categorified quantum gl(2).
