论文标题
部分包裹的福卡亚类别和表面切割的回忆
Recollements of partially wrapped Fukaya categories and surface cuts
论文作者
论文摘要
在本文中，我们使用回忆来调查具有标记点的部分包裹的表面类别。特别是，我们表明切割表面会引起对相应部分包裹的福卡亚类别的回忆。我们的方法是基于以下事实：具有标记点的表面的部分包裹的福卡亚类别是三角形的，等于Haiden，Katzarkov和Kontsevich所示，具有同源平滑且适当的柔和的代数的完美衍生类别，具有零差分。使用此过程，我们研究了部分包裹的福卡亚类别的特定发电机，即完整的例外序列，淤积对象和简单的集合。特别是，我们充分表征了完整的特殊序列的存在，并给出了一个部分包裹的福卡亚类别的示例，该类别不承认一个没有正面自我扩展的生成器。
In this paper we use recollements to investigate partially wrapped Fukaya categories of surfaces with marked points. In particular, we show that cutting surfaces gives rise to recollements of the corresponding partially wrapped Fukaya categories. Our approach is based on the fact that the partially wrapped Fukaya category of a surface with marked points is triangle equivalent to the perfect derived category of a homologically smooth and proper graded gentle algebra with zero differential as shown by Haiden, Katzarkov and Kontsevich. Using this, we study particular generators of partially wrapped Fukaya categories, namely full exceptional sequences, silting objects and simple-minded collections. In particular, we fully characterise the existence of full exceptional sequences and we give an example of a partially wrapped Fukaya category which does not admit a silting object, that is a generator with no positive self-extensions.
