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- Title
FUNDAMENTAL BIQUANDLES OF RIBBON 2-KNOTS AND RIBBON TORUS-KNOTS WITH ISOMORPHIC FUNDAMENTAL QUANDLES.
- Authors
ASHIHARA, SOSUKE
- Abstract
The fundamental quandles and biquandles are invariants of classical knots and surface knots. It is unknown whether there exist classical or surface knots which have isomorphic fundamental quandles and distinct fundamental biquandles. We show that ribbon 2-knots or ribbon torus-knots with isomorphic fundamental quandles have isomorphic fundamental biquandles. For this purpose, we give a method for obtaining a presentation of the fundamental biquandle of a ribbon 2-knot/torus-knot from its fundamental quandle.
- Subjects
KNOT theory; INVARIANTS (Mathematics); ISOMORPHISM (Mathematics); RIBBON theory; TORUS knots; FUNDAMENTAL groups (Mathematics); MATHEMATICS
- Publication
Journal of Knot Theory & Its Ramifications, 2014, Vol 23, Issue 1, p-1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216514500011