Mutual arc presentations and braided open books

It remains an open problem whether every fibered link in the 3-sphere is the binding of a braided open book; a positive answer to this question would prove a conjecture of Montesinos and Morton. While braided open books generalize braids, we introduce mutual arc presentations as a natural generalization of arc presentations of links in 3-manifolds. We show that if a fibered link admits a mutual arc presentation, then it is the binding of a braided open book. Moreover, we prove that this holds for all fibered links in the 3-sphere whose fiber surfaces can be obtained via Seifert’s algorithm.