A groupoid rack and spatial surfaces
Abstract
A spatial surface is a compact surface embedded in the $3$-sphere. We assume that each connected component has non-empty boundary. Spatial surfaces are represented by diagrams of spatial trivalent graphs. In this paper, we introduce the notion of a groupoid rack, which is an algebraic structure that can be used for colorings of diagrams of oriented spatial surfaces. Furthermore, we show that the groupoid rack has a universal property on colorings for diagrams of spatial surfaces.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2023
- DOI:
- 10.48550/arXiv.2310.06423
- arXiv:
- arXiv:2310.06423
- Bibcode:
- 2023arXiv231006423A
- Keywords:
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- Mathematics - Geometric Topology
- E-Print:
- 13 pages, 10 figures