Agniva Roy: Spinal open books and symplectic fillings with exotic fibers

Agniva Roy (Boston College)

Title: Spinal open books and symplectic fillings with exotic fibers

Abstract: The question of understanding symplectic fillings of contact 3-manifolds has a rich history and deep connections to various aspects of low-dimensional topology, such as exotic 4-manifolds, mapping class groups of surfaces, complex geometry, algebraic singularities, among others. The technique of spinal open books, recently introduced by Lisi - Van Horn-Morris - Wendl, describes strong symplectic fillings of planar spinal manifolds in terms of foliations by pseudoholomorphic curves. These foliation descriptions, in the broadest generality, contain singular curves, which are Lefschetz-type singularities, and also a new phenomenon called exotic curves. In the Lefschetz-amenable setting, exotic curves disappear, and fillings can be classified as Lefschetz fibrations, depending on the number of singular curves. In joint work with Hyunki Min and Luya Wang, we give a topological description of the exotic curves in terms of identifying them with a local model, give a count of exotic fibers in any filling, and use these to classify symplectic fillings of certain planar spinal open books that are not Lefschetz-amenable.