A groupoid rack and spatial surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910839508828160 |
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| author | Arai, Katsunori |
| author_facet | Arai, Katsunori |
| contents | A spatial surface is a compact surface embedded in the $3$-sphere. We assume that a spatial surface is oriented and that each connected component of a spatial surface is neither a disk nor without a boundary. A diagram of a spatial surface is a diagram of a spatial trivalent graph that is a spine of the spatial surface. In this paper, we introduce the notion of a groupoid rack, which is used for considering colorings for diagrams of spatial surfaces in order to obtain an invariant of spatial surfaces. Furthermore, we show that a groupoid rack has a universal property on colorings for diagrams of spatial surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06423 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A groupoid rack and spatial surfaces Arai, Katsunori Geometric Topology A spatial surface is a compact surface embedded in the $3$-sphere. We assume that a spatial surface is oriented and that each connected component of a spatial surface is neither a disk nor without a boundary. A diagram of a spatial surface is a diagram of a spatial trivalent graph that is a spine of the spatial surface. In this paper, we introduce the notion of a groupoid rack, which is used for considering colorings for diagrams of spatial surfaces in order to obtain an invariant of spatial surfaces. Furthermore, we show that a groupoid rack has a universal property on colorings for diagrams of spatial surfaces. |
| title | A groupoid rack and spatial surfaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2310.06423 |