Spinal open books and symplectic fillings
speaker: Luya Wang (Stanford University)abstract: Pseudoholomorphic curves are often useful in showing uniqueness and finiteness for classification problems of symplectic manifolds. In a series of works, Wendl used punctured pseudoholomorphic foliations to provide classifications of symplectic fillings of contact three-manifolds supported by planar open books. In a joint work in progress with Hyunki Min and Agniva Roy, we build on the works of Lisi--Van Horn-Morris--Wendl in using spinal open books to further delve into the classification problem of higher genus open books. In particular, we provide the local model of "exotic fibers" in a generalized version of Lefschetz fibrations, arising from pseudoholomorphic foliations associated to spinal open books. As a sample application, we show that strongly fillable parabolic torus bundles supported by non-Lefschetz-amendable spinal open books have unique minimal strong fillings which are deformation equivalent to Stein fillings.
timetable:
Mon 3 Jun, 11:00 - 12:00, Aula Dini
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