Joint IAS/Princeton/Columbia Symplectic Geometry Seminar
Functors and relations from Fukaya categories of LG models
The Fukaya category of a Landau-Ginzburg (LG) model $W: E \to C$, denoted $F(E,W)$, enlarges the Fukaya category of $E$ to include certain non-compact Lagrangians determined by $W$ (for instance, Lefschetz fibrations and their thimbles). I will describe natural functors associated to the Fukaya categories of $(E,W)$ and the general fibre $M$, and introduce a new Floer homology ring for $(E,W)$. Using these, I will explain two new results: (a) a generation criterion for $F(E,W)$, in the sense of Abouzaid/AFOOO, and (b) exact triangles of functors, one each in $F(E,W)$ and $F(M)$. First applications include stability and generation results for Fukaya categories and a new proof of exact sequences for fibered twists. This is joint work (in preparation) with Mohammed Abouzaid.