论文标题
从镜子对称性分类的结，第一部分：连贯的滑轮
Knot Categorification from Mirror Symmetry, Part I: Coherent Sheaves
论文作者
论文摘要
我们得出了两种几何方法，以分类与任意紧凑的简单谎言组$^l {g} $相关的链接的量子不变性。在第一部分中，我们根据$ {\ cal x} $上的等效性类别的类别描述了第一种方法，即单数$ g $ - 单极的模量空间，其中$ g $与兰格兰兹二元的$^lg $有关。在第二部分中，我们基于与潜在$ W $的Calabi-yau $ y $ fukaya-seidel类别的衍生类别描述第二种方法。这两种方法与镜面对称性的版本相关，该版本在故事中起着至关重要的作用。在第三部分中，我们解释了这些结果的字符串理论来源，以及与Witten引起的方法的关系。
We derive two geometric approaches to categorification of quantum invariants of links associated to an arbitrary compact simple Lie group $^L{G}$. In part I, we describe the first approach, based on an equivariant derived category of coherent sheaves on ${\cal X}$, the moduli space of singular $G$-monopoles, where $G$ is related to $^LG$ by Langlands duality. In part II, we describe the second approach, based on the derived category of a Fukaya-Seidel category of a Calabi-Yau $Y$ with potential $W$. The two approaches are related by a version of mirror symmetry, which plays a crucial role in the story. In part III, we explain the string theory origin of these results, and the relation to an approach due to Witten.
