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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.01627 |
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| _version_ | 1866909765384273920 |
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| author | Benway, Ian |
| author_facet | Benway, Ian |
| contents | Work of Kalelkar, Schleimer, and Segerman shows that, with some exceptions, the set of essential ideal triangulations of an orientable cusped hyperbolic 3-manifold is connected via 2-3 and 3-2 moves. It is natural to ask if the subgraph consisting of only those triangulations that are geometric is connected. Hoffman gives the first two examples of geometric triangulations with the property that no 2-3 or 3-2 move results in a geometric triangulation. In this paper, we introduce these as isolated geometric triangulations and show that this is not a property of small manifolds by exhibiting an infinite family of once-punctured torus bundles whose monodromy ideal triangulation is isolated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01627 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Isolated Geometric Triangulations Benway, Ian Geometric Topology Work of Kalelkar, Schleimer, and Segerman shows that, with some exceptions, the set of essential ideal triangulations of an orientable cusped hyperbolic 3-manifold is connected via 2-3 and 3-2 moves. It is natural to ask if the subgraph consisting of only those triangulations that are geometric is connected. Hoffman gives the first two examples of geometric triangulations with the property that no 2-3 or 3-2 move results in a geometric triangulation. In this paper, we introduce these as isolated geometric triangulations and show that this is not a property of small manifolds by exhibiting an infinite family of once-punctured torus bundles whose monodromy ideal triangulation is isolated. |
| title | On Isolated Geometric Triangulations |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2509.01627 |