CALCULATING THE FUNDAMENTAL BIQUANDLES OF SURFACE LINKS FROM THEIR CH–DIAGRAMS

Abstract

The fundamental biquandle is an invariant of an oriented surface link, which is defined by a presentation obtained from a surface diagram of the surface link: The generating set consists of labels of the semi-sheets and the relator set consists of relations defined at the double point curves. Any surface link can be presented by a link diagram with some markers which is called a ch-diagram. Using this fact, we give a method for calculating the fundamental biquandle of a surface link from its ch-diagram directly.