Sectorial descent for wrapped Fukaya categories
Abstract
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 socalled 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 FukayaSeidel category of a Lefschetz fibration with Weinstein 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.03427
 Bibcode:
 2018arXiv180903427G
 Keywords:

 Mathematics  Symplectic Geometry
 EPrint:
 143 pages, 29 figures