Combinatorial Characterizations and Branched Manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915538553274368 |
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| author | Cooper, Daryl Mavrakis, Leslie Patel, Priyam |
| author_facet | Cooper, Daryl Mavrakis, Leslie Patel, Priyam |
| contents | A family of compact n-manifolds is locally combinatorially defined (LCD) if it can be specified by a finite number of local triangulations. We show that LCD is equivalent to the existence of a compact branched n-manifold W, such that the family is precisely those manifolds that immerse into W. In subsequent papers, the equivalence will be used to show that, for each of the eight Thurston geometries, the family of closed 3-manifolds admitting that geometry is LCD. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorial Characterizations and Branched Manifolds Cooper, Daryl Mavrakis, Leslie Patel, Priyam Geometric Topology Combinatorics 57Q99 A family of compact n-manifolds is locally combinatorially defined (LCD) if it can be specified by a finite number of local triangulations. We show that LCD is equivalent to the existence of a compact branched n-manifold W, such that the family is precisely those manifolds that immerse into W. In subsequent papers, the equivalence will be used to show that, for each of the eight Thurston geometries, the family of closed 3-manifolds admitting that geometry is LCD. |
| title | Combinatorial Characterizations and Branched Manifolds |
| topic | Geometric Topology Combinatorics 57Q99 |
| url | https://arxiv.org/abs/2510.06514 |