Microlocal Morse theory of wrapped Fukaya categories

By Sheel Ganatra, J. Pardon, Vivek V. Shende. Annals of Mathematics, 2018

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Consider on the one hand the partially wrapped Fukaya category of a cotangent bundle stopped at an appropriately stratifiable singular isotropic. Consider on the other hand the derived category of sheaves with microsupport along the singular isotropic. We show here that the former is equivalent to the compact objects of the latter. Applications include a sheaf-theoretic description of the wrapped Fukaya categories of plumbings and of codimension one Weinstein hypersurfaces of cosphere bundles. While inspired by the Nadler-Zaslow correspondence, our results do not depend on it.

Subfields: Radiology, Nuclear Medicine and Imaging, Spectroscopy

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