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 construct more than one strong symplectic filling of the link of the $A_k$-type singularity. 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.

arXiv comment27 pages, 5 figures

References in corpus (6)

• Geometry of contact transformations and domains: orderability versus squeezing
• Lagrangian matching invariants for fibred four-manifolds: II
• The topology of Stein fillable manifolds in high dimensions I
• Symplectic surgeries from singularities
• On symplectic fillings of spinal open book decompositions I: Geometric constructions
• Symplectic Mapping Class Group Relations Generalizing the Chain Relation