Lefschetz fibrations and their Fukaya categories

From Talbot

We want to have an approximate definition of symplectic Lefschetz fibration; the definition of vanishing cycles; the action of the braid group on exceptional collections; and the directed Fukaya category.

Derived invariance of the directed Fukaya category should then be stated without proof - for intuition, one can refer to the previous talk on exceptional collections.

Sources are Auroux' "monodromy invariants in symplectic topology" as well as "vanishing cycles and mutation" (note: the terminology in the latter is definitely out of date, and should be avoided).