Mutual arc presentations and braided open books

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.

24 pages, 12 figures