Exercises for Mini-course on the Fukaya Category
نویسندگان
چکیده
(1) Give a purely combinatorial definition of the Floer cochain complex (CF (L0, L1), ∂) over ΛZ2 . In particular, prove that ∂ 2 = 0. (2) Now do the same, but over ΛK where K is an arbitrary field (not necessarily of characteristic 2). (3) How far can the conditions on the Li be relaxed? Can they be immersed curves, or nullhomotopic curves? (4) More generally, let L0, . . . , Lk be transversely-intersecting curves as above. Give a purely combinatorial definition of the A∞ structure map m : CF (Lk−1, Lk)⊗ . . .⊗ CF (L0, L1)→ CF (L0, Lk), and prove that the maps defined in this way satisfy the A∞ relations (start by working over a Novikov field of characteristic 2 as before, then generalize to arbitrary characteristic).
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