Consider the Fukaya category associated to a Lefschetz fibration. It turns out that the Floer cohomology of the monodromy around ∞ gives rise to natural transformations from the Serre functor to the identity functor, in that category. We pay particular attention to the implications of that idea for Lefschetz pencils.
Mathematics Subject Classification (2010).
- primary 53D40; secondary 53D12
- Floer homology
- Lefschetz fibrations
- Fukaya categories