Research ArticleNo Access

Almost all strongly quasipositive braid closures are fibered

Mathematisches Institut, Universität Bern, Sidlerstrasse 5, Bern CH-3012, Switzerland

https://doi.org/10.1142/S0218216522500730Cited by:1 (Source: Crossref)

Abstract

We use the Birman–Ko–Lee presentation of the braid group to show that all closures of strongly quasipositive braids whose normal form contains a positive power of the dual Garside element $δ$ are fibered. We classify links which admit such a braid representative in geometric terms as boundaries of plumbings of positive Hopf bands to a disk. Rudolph constructed fibered strongly quasipositive links as closures of positive words on certain generating sets of $B_{n}$ and we prove that Rudolph’s condition is equivalent to ours. Finally, we show that the braid index is a strict upper bound for the number of crossing changes required to fiber a strongly quasipositive braid.

Keywords:

AMSC: 57K10

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