A symplectic basis for 3-manifold triangulations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866918132189233152 |
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| author | Mathews, Daniel V. Purcell, Jessica S. |
| author_facet | Mathews, Daniel V. Purcell, Jessica S. |
| contents | In the 1980s, Neumann and Zagier introduced a symplectic vector space associated to an ideal triangulation of a cusped 3-manifold, such as a knot complement. We give a geometric interpretation for this symplectic structure in terms of the topology of the 3-manifold, via intersections of certain curves on a Heegaard surface. We also give an algorithm to construct curves forming a symplectic basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_06969 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A symplectic basis for 3-manifold triangulations Mathews, Daniel V. Purcell, Jessica S. Geometric Topology 57K30, 57K31 In the 1980s, Neumann and Zagier introduced a symplectic vector space associated to an ideal triangulation of a cusped 3-manifold, such as a knot complement. We give a geometric interpretation for this symplectic structure in terms of the topology of the 3-manifold, via intersections of certain curves on a Heegaard surface. We also give an algorithm to construct curves forming a symplectic basis. |
| title | A symplectic basis for 3-manifold triangulations |
| topic | Geometric Topology 57K30, 57K31 |
| url | https://arxiv.org/abs/2208.06969 |