Universal Lefschetz fibrations over bounded surfaces

TL;DR

This paper introduces the concepts of universal and strongly universal Lefschetz fibrations over bounded surfaces, providing characterizations and explicit constructions for certain fibers, and deriving related immersion results for 4-dimensional 2-handlebodies.

Contribution

It defines and characterizes universal Lefschetz fibrations and constructs explicit examples for specific fibers and base surfaces.

Findings

Constructed strongly universal Lefschetz fibrations for torus and orientable surfaces with boundary

Provided characterization criteria for universal Lefschetz fibrations

Derived immersion results for 4-dimensional 2-handlebodies

Abstract

In analogy with the vector bundle theory we define universal and strongly universal Lefschetz fibrations over bounded surfaces. After giving a characterization of these fibrations we construct very special strongly universal Lefschetz fibrations when the fiber is the torus or an orientable surface with connected boundary and the base surface is the disk. As a by-product we also get some immersion results for 4-dimensional 2-handlebodies.