Nearly fibered links with genus one

We classify all then-component links in the 3-sphere that bounda Thurston norm minimizing Seifert surface S with Euler characteristicX(Sigma) =n-2 and that are nearly fibered, which means that the rank of their link Floerhomology group<^> HFL in the maximal (collapsed) Alexander grading stopis equalto two. In other words, such a linkLsatisfiesstop=n-?(S)2= 1, and in additionr k<^> HFL*(L)[1] = 2 and rk<^>HFL*(L)[s] = 0 for everys>1.The proof of the main theorem is inspired by the one of a similar recent result for knots by Baldwin and Sivek, and involves techniques from sutured Floerhomology. Furthermore, we also compute the group<^> HFLfor each of these links.