Lefschetz–Bott Fibrations on Line Bundles Over Symplectic Manifolds
Abstract We describe Lefschetz–Bott fibrations on complex line bundles over symplectic manifolds explicitly. As an application, we show that the link of the $A_{k}$-type singularity has more than one strong symplectic filling up to homotopy and blow-up at points when the dimension of the link is greater than or equal to $5$. In the appendix, we show that the total space of a Lefschetz–Bott fibration over the unit disk serves as a strong symplectic filling of a contact manifold compatible with an open book induced by the fibration.