Spinal open book decompositions and symplectic fillings
Recently, C. Wendl used holomorphic curves to show that any
strong filling of a planar open book comes as an extension of the open
book to a Lefschetz fibration of the filling. I'll discuss a
generalization of this result to spinal open books and discuss some
applications, including the classification of symplectic fillings of
the lens spaces L(p,1) and a determination of fillability for contact
structures on circle bundles. Part of this is joint with O.
Plamenevskaya and part of this is joint with S. Lisi and C.