Japan Society for the Promotion of Science:Grants-in-Aid for Scientific Research
Date (from‐to) : 2011 -2013
Author : KAMADA SEIICHI; SAEKI Osamu; OHTSUKI Tomotada; KAMADA Naoko
As generalizations of a quandle, we studied biquandles and symmetric quandles. The notion of a biquandle was re-defined by a system of axioms, and two additional structures, called T-structure and V-structure, were introduced. These structures are related to virtual knots and twisted virtual knots. We also gave a method of constructing a biquandle from a given quandle. By the method, one can easily and effectively construct many biquandles. Presentation of a symmetric quandle was studied, and a method of obtaining a presentation of the fundamental symmetric quandle of a manifold knot was introduced.