Mutual arc presentations and braided open books

Chun-Sheng Hsueh (Humboldt-Universität zu Berlin)

Monday 26th January 15:00-16:00
Maths 311B

Abstract

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.

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