Mutual arc presentations and braided open books

TL;DR

This paper proves that all canonically fibered links in the 3-sphere can be realized as bindings of braided open books, introduces mutual arc presentations as a key tool, and constructs new examples of such links.

Contribution

It establishes that every canonically fibered link admits a braided open book presentation and introduces mutual arc presentations as a novel technical approach.

Findings

Every canonically fibered link in S^3 is the binding of a braided open book.

Mutual arc presentations are effective for representing fibered links.

New fibered links are constructed via connected sum and cabling, expanding known examples.

Abstract

We show that every canonically fibered link in $S^3$ is the binding of a braided open book in $S^3$, addressing a question of Montesinos and Morton. We introduce mutual arc presentations as our main technical tool, which we consider to be of independent interest. We prove that any fibered link admitting such a presentation is the binding of a braided open book. Furthermore, new examples of fibered links serving as bindings of braided open books are obtained via connected sum and cabling operations, thereby providing examples of bindings of braided open books that are not canonically fibered.