On nearly Lefschetz fibrations and spinal open books

Abstract

We survey the recent development of spinal open books and nearly Lefschetz fibrations. The focus is on explaining past and new results regarding the detection of symplectic fillability and classification of symplectic fillings of contact 3-manifolds in light of the new machinery. We give many examples and a list of open questions. This can be considered as an additional chapter to the lecture notes by Ozbacgi and Wendl.