Yoshiyuki Yokota

Examples of tunnel number one knots which have the property ‘1 + 1 = 3’

Let K be a knot in the 3-sphere S 3 , N ( K ) the regular neighbourhood of K and E ( K ) = cl(S 3 − N ( K )) the exterior of K . The tunnel number t ( K ) is the minimum number of mutually disjoint arcs properly embedded in E ( K ) such that the complementary space of a regular neighbourhood of the arcs is a handlebody. We call the family of arcs satisfying this condition an unknotting tunnel system for K . In particular, we call it an unknotting tunnel if the system consists of a single arc.

The Kauffman polynomial of alternating links

Abstract Let D be an alternating diagram and Λ D (a, z) e Z [a ± 1 , z ± 1 ] the regular isotopy invariant of D introduced by L.H. Kauffman. With respect to variable a , the maximal and minimal degrees of Λ D ( a , z ) are given. Furthermore, it will be shown that the shape of D is strongly reflected in the coefficient polynomials at the maximal and minimal powers of a .

Polynomial invariants of periodic knots

We give a new criterion for the periodicity of knots combining the skein and Kauffman polynomials which extends the old results using the polynomials individually.