Lefschetz fibrations on cotangent bundles and some plumbings

TL;DR

This paper develops a method to construct Lefschetz fibrations on Weinstein manifolds using handle decompositions, with applications to cotangent bundles and plumbings, revealing diffeomorphic relationships among certain singularity Milnor fibers.

Contribution

It introduces a novel approach to building Lefschetz fibrations from handle decompositions and applies it to specific manifolds, establishing new diffeomorphism results.

Findings

Diffeomorphic families of plumbing spaces identified

Milnor fibers of certain singularities shown to be diffeomorphic in odd dimensions

New connections between handle decompositions and Lefschetz fibrations established

Abstract

We introduce an idea of constructing Lefschetz fibrations of Weinstein manifolds from Weinstein handle decompositions on them. We prove theorems that formulate the idea for the cases of cotangent bundles and some plumbings. As a corollary, we give diffeomorphic families of plumbing spaces. Those diffeomorphic families contain some plumbing spaces with names. For example, Milnor fibers of $A_{4k+3}$ and $D_{4k+3}$ singularities are diffeomorphic if their complex dimension is odd.