What references are there for learning Fukaya categories (specifically, good references for self-study)?
In addition, any references with an eye toward homological mirror symmetry would be greatly appreciated.
2026-02-23 09:03:49.1771837429
Reference for Fukaya Categories and Homological Mirror Symmetry
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I personally recommend Paul Seidel's Fukaya Categories and Picard-Lefschetz Theory book. It is not easy (imho) but contains an introduction to $A_\infty$-categories, it explains the Fukaya categories in both a preliminary and a complete version and provides an example of Fukaya cat. of a Lefschetz fibration.
Another good reference is the paper
http://arxiv.org/pdf/math/0011041.pdf
Section 4 is about $A_\infty$-structures, while section5 contains an introduction to Fukaya categories.