Lefschetz fibrations on cotangent bundles and some plumbings.

We would like to construct Lefschetz fibrations on Weinstein manifolds based on the Weinstein structures on them. As the first step, we construct an algorithm producing Lefschetz fibrations of cotangent bundles from handle decompositions of the zero sections. If the zero section is of dimension two, then the constructed Lefschetz fibrations are connected to each other by four moves which are deformation, cyclic permutation, Hurwitz move, and stabilization. Moreover, as an application, we construct Lefschetz fibrations of some plumbing spaces of cotangent bundles.