Let L be an oriented link with an alternating diagram D. It is known that
L is a fibered link if and only if the surface R obtained by applying
Seifert's algorithm to D is a Hopf plumbing. Here, we call R a Hopf
plumbing if R is obtained by successively plumbing finite number of Hopf
bands to a disk.
In this paper, we discuss its extension so that we show the following
theorem. Let R be a Seifert surface obtained by applying Seifert's algorithm
to an almost alternating diagrams. Then R is a fiber surface if and only if
R is a Hopf plumbing.
We also show that the above theorem can not be extended to 2-almost
alternating diagrams, that is, we give examples of 2-almost alternating
diagrams for knots whose Seifert surface obtained by Seifert's algorithm are
fiber surfaces that are not Hopf plumbing. This is shown by using a criterion
of Melvin-Morton.Comment: 18 pages, 30 figure