Lefschetz fibrations over the disc

TL;DR

This paper establishes a comprehensive set of moves connecting any two Lefschetz fibrations over the disk with the same 4-dimensional 2-handlebody, also relating diffeomorphic open books, offering a new perspective on existing results.

Contribution

It introduces a complete set of moves for Lefschetz fibrations over the disk, linking them to 3D open books and providing an alternative proof to Harer's result.

Findings

Complete move set for Lefschetz fibrations over the disk

Moves relating diffeomorphic 3D open books

New approach to existing topological results

Abstract

We provide a complete set of moves relating any two Lefschetz fibrations over the disk having as their total space the same 4-dimensional 2-handlebody up to 2-equivalence. As a consequence, we also obtain moves relating diffeomorphic 3-dimensional open books, providing a different approach to an analogous previous result by Harer.