Braided open book decompositions in S3
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Benjamin Bode [1]
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[1] Instituto de Ciencias Matemáticas
Instituto de Ciencias Matemáticas
Madrid, España
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- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 6, 2023, págs. 2187-2232
- Idioma: inglés
- DOI: 10.4171/RMI/1429
- Enlaces
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Resumen
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 S3 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.
