Combinatorial description of closed $3$-manifolds via ordered ideal triangulations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917543091896320 |
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| author | Garoufalidis, Stavros Kashaev, Rinat Suzuki, Sakie |
| author_facet | Garoufalidis, Stavros Kashaev, Rinat Suzuki, Sakie |
| contents | It is well known that every compact oriented 3-manifold admits an ideal triangulation, and that any two such triangulations with at least two ideal tetrahedra are related by a sequence of Pachner $2$-$3$ moves. Motivated by constructions in quantum topology, we give a combinatorial description of closed $3$-manifolds in terms of ordered ideal triangulations and ordered Pachner $2$-$3$ and $0$-$2$ moves. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_29443 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Combinatorial description of closed $3$-manifolds via ordered ideal triangulations Garoufalidis, Stavros Kashaev, Rinat Suzuki, Sakie Geometric Topology 57K30, 57K31, 57K16 It is well known that every compact oriented 3-manifold admits an ideal triangulation, and that any two such triangulations with at least two ideal tetrahedra are related by a sequence of Pachner $2$-$3$ moves. Motivated by constructions in quantum topology, we give a combinatorial description of closed $3$-manifolds in terms of ordered ideal triangulations and ordered Pachner $2$-$3$ and $0$-$2$ moves. |
| title | Combinatorial description of closed $3$-manifolds via ordered ideal triangulations |
| topic | Geometric Topology 57K30, 57K31, 57K16 |
| url | https://arxiv.org/abs/2605.29443 |