Braided open book decompositions in

  • Benjamin Bode

    nstituto de Ciencias Matemáticas (ICMAT), Madrid, Spain
Braided open book decompositions in $S^3$ cover
Download PDF

This article is published open access under our Subscribe to Open model.


We study four (a priori) different ways in which an open book decomposition of the 3-sphere can be defined to be braided. These include generalised exchangeability defined by Morton and Rampichini and mutual braiding defined by Rudolph, which were shown to be equivalent by Rampichini, as well as P-fiberedness and a property related to simple branched covers of inspired by work of Montesinos and Morton. We prove that these four notions of a braided open book are actually all equivalent to each other. We show that all open books in the 3-sphere whose binding has a braid index of at most 3 can be braided in this sense. We relate our findings to a conjecture on real algebraic links by Benedetti and Shiota and to a stronger version of Harer’s conjecture due to Montesinos and Morton.

Cite this article

Benjamin Bode, Braided open book decompositions in . Rev. Mat. Iberoam. 39 (2023), no. 6, pp. 2187–2232

DOI 10.4171/RMI/1429