Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424669 | Topology and its Applications | 2015 | 10 Pages |
Abstract
Racks do not give us invariants of surface-knots in general. For example, if a surface-knot diagram has branch points (and a rack which we use satisfies some mild condition), then it admits no rack colorings. In this paper, we investigate rack colorings for surface-knot diagrams without branch points and prove that rack colorings are invariants of S2-knots. We also prove that rack colorings for S2-knots can be interpreted in terms of quandles, and discuss a relationship with regular-equivalences of surface-knot diagrams.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Kanako Oshiro, Kokoro Tanaka,