1999/04/09 by Hiroshi Goda, Goda, Hiroshi, Mikami Hirasawa +3 · 1 citation
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/9904043
18 pages, 30 figures
arxiv created 1999/04/09 · arxiv updated 2009/11/30
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.