The fundamental quandle of ribbon concordances
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917293208895488 |
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| author | Horvat, Eva Marčič, Luka |
| author_facet | Horvat, Eva Marčič, Luka |
| contents | We describe the fundamental quandle of a properly embedded surface $F$ (possibly with boundary) in $\mathbb{R} ^{3}\times I$, and derive its presentation in terms of a motion picture diagram or a CH-diagram of $F$. Our study is based on the topological definition of the fundamental quandle. We prove that a ribbon concordance $C$ from a classical knot $K_1$ to $K_0$ gives rise to an injective quandle homomorphism $Q(K_0)\to Q(C)$ and a surjective quandle homomorphism $Q(K_1)\to Q(C)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20841 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The fundamental quandle of ribbon concordances Horvat, Eva Marčič, Luka Geometric Topology 57K10 (Primary) 57K12, 57K45 (Secondary) We describe the fundamental quandle of a properly embedded surface $F$ (possibly with boundary) in $\mathbb{R} ^{3}\times I$, and derive its presentation in terms of a motion picture diagram or a CH-diagram of $F$. Our study is based on the topological definition of the fundamental quandle. We prove that a ribbon concordance $C$ from a classical knot $K_1$ to $K_0$ gives rise to an injective quandle homomorphism $Q(K_0)\to Q(C)$ and a surjective quandle homomorphism $Q(K_1)\to Q(C)$. |
| title | The fundamental quandle of ribbon concordances |
| topic | Geometric Topology 57K10 (Primary) 57K12, 57K45 (Secondary) |
| url | https://arxiv.org/abs/2602.20841 |