Almost all strongly quasipositive braid closures are fibered

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 $\delta$ 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.