Filtered Fukaya categories

Abstract

We upgrade the natural weakly-filtered structure of Fukaya categories discussed in arXiv:1806.06630 to a genuinely filtered one. The main tools are a Morse-Bott, or 'cluster', model for Fukaya categories and a particular choice of class of perturbation data. We also include the construction of continuation $A_{\infty }$-functors following arXiv:1604.02540v2 in the context of filtered Fukaya categories.

54 pages. Revised version accepted for publication on Journal of Symplectic Geometry