Takahiro Oba

Non-isomorphic higher-dimensional Lefschetz fibrations over the disk

Higher-dimensional Lefschetz fibrations over the disk play an important role in the study of Weinstein/Stein domains. It is known that Lefschetz bifibrations are one of useful tools to construct higher-dimensional Lefschetz fibrations over the disk. Briefly, a Lefschetz bifibration is a Lefschetz fibration whose fibers admit Lefschetz fibrations. In this talk, by using Lefschetz bifibrations, we construct an infinite family of higher-dimensional Lefschetz fibrations over the disk such that they are pairwise non-isomorphic and induces the same open book decomposition on their boundaries. As a corollary, we obtain an infinite family of higher-dimensional contact manifolds each of which admits infinitely many pairwise homotopy inequivalent Stein fillings.