Building Three-Dimensional Differentiable Manifolds Numerically II: Limitations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917557791883264 |
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| author | Lindblom, Lee Rinne, Oliver |
| author_facet | Lindblom, Lee Rinne, Oliver |
| contents | Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by expanding the class of suitable triangulations, significantly increasing the number of manifolds to which these methods apply. These new results show that this expanded class of triangulations is still a small subset of all possible triangulations. This demonstrates that fundamental changes to these methods are needed to further expand the collection of manifolds on which differentiable structures can be constructed numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01276 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Building Three-Dimensional Differentiable Manifolds Numerically II: Limitations Lindblom, Lee Rinne, Oliver General Relativity and Quantum Cosmology Mathematical Physics Methods were developed in Ref. [1] for constructing reference metrics (and from them differentiable structures) on three-dimensional manifolds with topologies specified by suitable triangulations. This note generalizes those methods by expanding the class of suitable triangulations, significantly increasing the number of manifolds to which these methods apply. These new results show that this expanded class of triangulations is still a small subset of all possible triangulations. This demonstrates that fundamental changes to these methods are needed to further expand the collection of manifolds on which differentiable structures can be constructed numerically. |
| title | Building Three-Dimensional Differentiable Manifolds Numerically II: Limitations |
| topic | General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2401.01276 |