Lefschetz-Bott fibrations on line bundles over symplectic manifolds

2019/01/15 Tue 15:00 - 16:30
Room 609, Building No.6
OBA, Takahiro

A Lefschetz–Bott fibration on a symplectic manifold is a smooth map to a surface with only Lefschetz–Bott critical points, which are modeled on Morse–Bott critical points. As Lefschetz fibrations have played an important role in the study of Stein fillings of contact manifolds, we expect Lefschetz–Bott fibrations to help us understand symplectic fillings of contact manifolds. However, little is known about symplectic manifolds admitting such fibrations. In this talk, we show that (complex) line bundles over some symplectic manifolds admit Lefschetz–Bott fibrations over the complex plane. Moreover using this, we discuss resolutions of some singularities and symplectic fillings of their links.