On rack colorings for surface-knot diagrams without branch points

Kanako Oshiro; Kokoro Tanaka

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arXiv · 1406.3543

On rack colorings for surface-knot diagrams without branch points

Kanako Oshiro·Kokoro Tanaka

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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 $S^2$-knots. We also prove that rack colorings for $S^2$-knots can be interpreted in terms of quandles, and discuss a relationship with regular-equivalences of surface-knot diagrams.

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Kanako Oshiro, Kokoro Tanaka. 2014-06-13. On rack colorings for surface-knot diagrams without branch points. https://arxiv.org/abs/1406.3543

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