Mutual arc presentations and braided open books
Benjamin Bode, Chun-Sheng Hsueh

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 is the binding of a braided open book in , 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Holomorphic and Operator Theory
