Arclike Lagrangians in Liouville sectors

Abstract: Sectorial descent, established in earlier work with Pardon-Shende, gives a local-to-global formula computing the wrapped Fukaya category of a Weinstein manifold from a sectorial cover. If one has a specific fixed global Lagrangian in mind that isn't contained in a single subsector, the resulting formula is only implicit, as it begins by appealing to the generation of this object by "local" Lagrangians. In this talk I will introduce and study the class of (global) "arclike" Lagrangian submanifolds with respect to a sectorial covering, which are allowed to run through subsector boundaries but in a controlled fashion. For arclike Lagrangians, a more explicit local-to-global analysis is possible. Based on works in progress with Hanlon-Hicks-Pomerleano-Sheridan and Hanlon-Hicks-Ward.