Essential surfaces derived from knot and link diagrams
by Makoto Ozawa
Abstract: Many knot classes of alternating, positive, Montesinos, adequate, homogeneous, algebraic, etc. are defined from knot and link diagrams, and essential surfaces in their complements are studied. In this talk, we define $\sigma$-adequate and $\sigma$-homogeneous knots and algebraically alternating knots which are extensions of the above knot classes, and describe essential surfaces in their complements.