Density of Fibers for the Filtered Fukaya Category of a Cotangent Bundle

A well-known result of Abouzaid says that the wrapped Fukaya category of a cotangent bundle is generated by one cotangent fiber. In the filtered case this is not true, but the filtered Fukaya category comes with a notion of interleaving distance. We will see that the iterated cones on the cotangent fibers generate a dense subcategory. The proof makes use of an embedding of the Fukaya category in the category of sheaves. This answers a question of Biran, who gave another proof with Ambrosioni and Cornea.

This is a joint work with Claude Viterbo and Bingyu Zhang.