Sectorial descent for wrapped Fukaya categories
Sectorial descent for wrapped Fukaya categories
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DOI：
10.1090/jams/1035
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发表时间：
2018-09
影响因子：
3.9
通讯作者：
Sheel Ganatra;J. Pardon;V. Shende
中科院分区：
文献类型：
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作者：
Sheel Ganatra;J. Pardon;V. Shende
我们开发了一套工具，用于在（部分）包装的福谷类别中进行计算。特别地，我们证明了（1）包裹福谷范畴关于所谓的Weinstein扇形覆盖的下降（cosheaf）性质和（2）Weinstein流形关于大多数Legendrian停止的部分包裹福谷范畴是由临界把手的余核和停止的连接圆盘生成的.我们还证明了（3）一个“停止去除等于局部化”的结果;（4）具有Liouville纤维的Lefschetz纤维化的P-S范畴是由Lefschetz顶针生成的。这些结果来自三个主要成分，也是独立的用途：：（5）一个Künneth公式（6）一个精确的三角形在福谷范畴与包装拉格朗日通过勒让德停止在无穷远和（7）一个几何准则时，向前推进函子之间的包装福谷范畴的刘维扇区是完全忠实的。
We develop a set of tools for doing computations in and of (partially) wrapped Fukaya categories. In particular, we prove (1) a descent (cosheaf) property for the wrapped Fukaya category with respect to so-called Weinstein sectorial coverings and (2) that the partially wrapped Fukaya category of a Weinstein manifold with respect to a mostly Legendrian stop is generated by the cocores of the critical handles and the linking disks to the stop. We also prove (3) a ‘stop removal equals localization’ result, and (4) that the Fukaya–Seidel category of a Lefschetz fibration with Liouville fiber is generated by the Lefschetz thimbles. These results are derived from three main ingredients, also of independent use: (5) a Künneth formula (6) an exact triangle in the Fukaya category associated to wrapping a Lagrangian through a Legendrian stop at infinity and (7) a geometric criterion for when a pushforward functor between wrapped Fukaya categories of Liouville sectors is fully faithful.