Kirby diagrams of 4-dimensional open books

TL;DR

This paper presents an algorithm to construct Kirby diagrams of 4-dimensional open books from Heegaard diagrams, and explores their diffeomorphism types under certain monodromy conditions.

Contribution

It introduces a method to derive Kirby diagrams from Heegaard diagrams and characterizes the diffeomorphism types of open books with trivial monodromy.

Findings

Algorithm for Kirby diagram construction from Heegaard diagrams

Open books with trivial monodromy are diffeomorphic to those with punctured handlebody pages

Characterization of monodromy as torus and sphere twists

Abstract

We provide an algorithm for constructing a Kirby diagram of a 4-dimensional open book given a Heegaard diagram of the page. As an application, we show that an open book constructed with arbitrary page and trivial monodromy is diffeomorphic to an open book constructed with a punctured handlebody as page and a composition of torus twists and sphere twists as monodromy.