TL;DR
This paper develops a genuinely filtered structure for Fukaya categories using Morse-Bott models and specific perturbation data, enhancing the algebraic framework for symplectic topology.
Contribution
It introduces a new genuinely filtered structure for Fukaya categories and constructs continuation $A_ infty$-functors within this framework.
Findings
Established a filtered Fukaya category structure
Constructed continuation $A_ infty$-functors in the filtered setting
Utilized Morse-Bott models for 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 -functors following arXiv:1604.02540v2 in the context of filtered Fukaya categories.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Black Holes and Theoretical Physics