Affiliation:
1. Department of Mathematics, Osaka Sangyo University, Nakagaito 3-1-1, Daito, Osaka 574, Japan
Abstract
We introduce a ribbon presentation to describe a ribbon knot, and equivalences between them. Superspun knots of classical knots are well known to be ribbon knots, and we give a construction of ribbon presentations of the knots by means of classical knot diagrams. We can then extend the classical Reidemeister moves into higher dimensions, and we prove that the presentations of a superspun knot are stably equivalent by using these moves.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
13 articles.
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1. Classification of ribbon 2-knots of 1-fusion with length up to six;Topology and its Applications;2021-09
2. Amphicheirality of ribbon 2-knots;Journal of Knot Theory and Its Ramifications;2020-08
3. Presentation of a ribbon 2-knot;Journal of Knot Theory and Its Ramifications;2020-06
4. Ribbon-clasp T2-knots and semi-welded knots;Journal of Knot Theory and Its Ramifications;2018-12
5. Ribbon crossing numbers, crossing numbers, and Alexander polynomials;Topology and its Applications;2018-09