SECTORIAL DESCENT FOR WRAPPED FUKAYA CATEGORIES

• 成果类型: Article
• 署名作者: Ganatra, Sheel; Pardon, John; Shende, Vivek
• 署名单位: University of Southern California; University of California System; University of California Berkeley; University of Southern Denmark
• 刊物名称: JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY
• ISSN/ISSBN: 0894-0347
• DOI: 10.1090/jams/1035
• 发表日期: 2024
• 页码: 499-635
• 关键词: lagrangian cobordisms; lefschetz fibrations; cotangent bundles; FLOER HOMOLOGY; exact sequence; CONSTRUCTION; MANIFOLDS; Duality; CURVES

摘要

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 K center dot unneth 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.