Fiberedness of almost-Montesinos knots

Abstract

In this paper we begin to classify fiberedness of "Almost-Montesinos" knots, a generalization of Montesinos knots. We employ the method used in the classification of fiberedness of Montesinos knots due to Hirasawa and Murasugi. To achieve this classification, we find minimal-genus surfaces of "skew pretzel links" (a generalization of pretzel links) via sutured manifold decompositions, following Gabai's method for pretzel links. We end by stating three remaining cases.