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For questions about Fukaya categories (as introduced by Fukaya in 1993) and their structure; consider also related tags such as [floer-homology] or [lagrangian-submanifolds].
5
votes
Generating Fukaya category vs split-generating Fukaya category
Yes, generation is stronger than split-generation, because you don't need to split off summands after forming iterated mapping cones with degree shifts.
The simplest example I have in mind is when $M$ …
10
votes
What is Known about the $K$-Theory of Fukaya Categories?
Let's say $X$ is an exact symplectic manifold, and $\pi:X\rightarrow\mathbb{C}$ is a Lefschetz fibration whose critical values are $z_1,\cdot\cdot\cdot,z_k\in\mathbb{C}$. Let $\gamma_1,\cdot\cdot\cdot …