Arc diagrams on 3-manifold spines
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911871841337344 |
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| author | Brand, Jack Burton, Benjamin A. Dancso, Zsuzsanna He, Alexander Jackson, Adele Licata, Joan |
| author_facet | Brand, Jack Burton, Benjamin A. Dancso, Zsuzsanna He, Alexander Jackson, Adele Licata, Joan |
| contents | We develop a theory of link projections to trivalent spines of 3-manifolds. We prove a Reidemeister Theorem providing a set of combinatorial moves sufficient to relate the projections of isotopic links. We also show that any link admits a crossingless projection to any special spine and we refine our theorem to provide a set of combinatorial moves sufficient to relate crossingless diagrams. Finally, we discuss the connection to Turaev's shadow world, interpreting our result as a statement about shadow equivalence of a class of 4-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_02007 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Arc diagrams on 3-manifold spines Brand, Jack Burton, Benjamin A. Dancso, Zsuzsanna He, Alexander Jackson, Adele Licata, Joan Geometric Topology 57K10, 57M15 We develop a theory of link projections to trivalent spines of 3-manifolds. We prove a Reidemeister Theorem providing a set of combinatorial moves sufficient to relate the projections of isotopic links. We also show that any link admits a crossingless projection to any special spine and we refine our theorem to provide a set of combinatorial moves sufficient to relate crossingless diagrams. Finally, we discuss the connection to Turaev's shadow world, interpreting our result as a statement about shadow equivalence of a class of 4-manifolds. |
| title | Arc diagrams on 3-manifold spines |
| topic | Geometric Topology 57K10, 57M15 |
| url | https://arxiv.org/abs/2202.02007 |