Quadruply-graded colored homology of knots
Quadruply-graded colored homology of knots
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DOI：
10.4064/fm30-11-2017
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发表时间：
2013-04
影响因子：
0.6
通讯作者：
E. Gorsky;S. Gukov;Marko Stosic
中科院分区：
文献类型：
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作者：
E. Gorsky;S. Gukov;Marko Stosic
我们猜想存在四个独立的分级有色HOMFLYPT同源性，并作出定性预测的各种有趣的结构和对称性的有色同源性的任意结。我们提出了一个明确的几何描述的矩形彩色同源环面结，并确定在这种情况下的新的分级。虽然其中一些结构在基于计数超对称配置（BPS状态，瞬子和涡旋）的结同源性的物理实现中具有自然的解释，但其他结构则是全新的。他们提出了新的几何和物理实现的有色HOMFLYPT同调作为Hochschild同调的范畴膜在朗道-金兹伯格B-模型，或等价地，在镜像A-模型。超群和超流形在这项工作的各个方面都令人惊讶地无处不在。
We conjecture the existence of four independent gradings in colored HOMFLYPT homology, and make qualitative predictions of various interesting structures and symmetries in the colored homology of arbitrary knots. We propose an explicit conjectural description for the rectangular colored homology of torus knots, and identify the new gradings in this context. While some of these structures have a natural interpretation in the physical realization of knot homologies based on counting supersymmetric configurations (BPS states, instantons, and vortices), others are completely new. They suggest new geometric and physical realizations of colored HOMFLYPT homology as the Hochschild homology of the category of branes in a Landau–Ginzburg B-model or, equivalently, in the mirror A-model. Supergroups and supermanifolds are surprisingly ubiquitous in all aspects of this work.