The Realization of 3D Topological Spaces Branched Over Graphs
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912534546612224 |
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| author | Duston, Christopher L |
| author_facet | Duston, Christopher L |
| contents | In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in dimension 3, and a complete set of the topological spaces branched over several graphs are found. We also include some new visualizations of the branched covering construction, in order to aid and clarify the understanding of how these structures can be used in quantum gravity to realize the topological nature of the spacetime foam. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Realization of 3D Topological Spaces Branched Over Graphs Duston, Christopher L General Relativity and Quantum Cosmology Mathematical Physics 83C45 (Primary), 57K30, 57K16, 81-04, 83C45 (Secondary) In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in dimension 3, and a complete set of the topological spaces branched over several graphs are found. We also include some new visualizations of the branched covering construction, in order to aid and clarify the understanding of how these structures can be used in quantum gravity to realize the topological nature of the spacetime foam. |
| title | The Realization of 3D Topological Spaces Branched Over Graphs |
| topic | General Relativity and Quantum Cosmology Mathematical Physics 83C45 (Primary), 57K30, 57K16, 81-04, 83C45 (Secondary) |
| url | https://arxiv.org/abs/2508.09026 |