Strongly quasipositive links with braid index 3 have positive Conway polynomial

Abstract

Strongly quasipositive links are those links which can be seen as closures of positive braids in terms of band generators. In this paper, we give a necessary condition for a link with braid index 3 to be strongly quasipositive, by proving that in that case, it has positive Conway polynomial (that is, all its coefficients are non-negative). We also show that this result cannot be extended to a higher number of strands, as we provide a strongly quasipositive braid whose closure has non-positive Conway polynomial.