Groups versus quandle-like invariants of 3-manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918150066405376 |
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| author | Ta, Luc |
| author_facet | Ta, Luc |
| contents | Risandles are nonassociative algebraic structures recently introduced to construct invariants of 3-manifolds. In this note, we show that the categories of groups and nonempty, faithful risandles are equivalent. In analogy to knot quandles, we also introduce fundamental risandles of 3-manifolds, which categorify the risandle coloring invariants of Ishii, Nakamura, and Saito. For infinitely many 3-manifolds, the equivalence of categories recovers the fundamental group from the fundamental risandle and vice versa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24098 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Groups versus quandle-like invariants of 3-manifolds Ta, Luc Geometric Topology Group Theory Quantum Algebra Primary 20N02, 57K31, Secondary 20J15, 57K12 Risandles are nonassociative algebraic structures recently introduced to construct invariants of 3-manifolds. In this note, we show that the categories of groups and nonempty, faithful risandles are equivalent. In analogy to knot quandles, we also introduce fundamental risandles of 3-manifolds, which categorify the risandle coloring invariants of Ishii, Nakamura, and Saito. For infinitely many 3-manifolds, the equivalence of categories recovers the fundamental group from the fundamental risandle and vice versa. |
| title | Groups versus quandle-like invariants of 3-manifolds |
| topic | Geometric Topology Group Theory Quantum Algebra Primary 20N02, 57K31, Secondary 20J15, 57K12 |
| url | https://arxiv.org/abs/2509.24098 |