Kirby diagrams of 4-dimensional open books

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.

27 pages, 38 figures; V2: Some clarifications, and modifications following a referee report. Final version, accepted for publication in Proceedings of the Edinburgh Mathematical Society

References in corpus (3)

• Right-veering diffeomorphisms of compact surfaces with boundary II
• An Algorithm taking Kirby diagrams to Trisection diagrams
• Trisecting a 4-dimensional book into three chapters