Almost Alternating Diagrams and Fibered Links in S 3

Let R be a Seifert surface obtained by applying Seifert's algorithm to a connected diagram D for a link L. In this paper, letting D be almost alternating, we give a practical algorithm to determine whether L is a fibered link and R is a fiber surface. We further show that L is a fibered link and R is a fiber surface for L if and only if R is a Hopf plumbing, that is, a successive plumbing of a finite number of Hopf bands. It has been known for some time that this is true if D is alternating, and we show that it is not always true if D is 2‐almost alternating. In the appendix, we partially answer C. Adams's open question concerning almost alternating diagrams. 2000 Mathematical Subject Classification : 57M25.