Estimating distances in simplicial complexes with applications to 3-manifolds and handlebody-knots
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915269869305856 |
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| author | Mondal, Sayantika Pongtanapaisan, Puttipong Vo, Hanh |
| author_facet | Mondal, Sayantika Pongtanapaisan, Puttipong Vo, Hanh |
| contents | We study distance relations in various simplicial complexes associated with low-dimensional manifolds. In particular, complexes satisfying certain topological conditions with vertices as simple multi-curves. We obtain bounds on the distances in such complexes in terms of number of components in the vertices and distance in the curve complex. We then define new invariants for closed 3-manifolds and handlebody-knots. These are defined using the splitting distance which is calculated using the distance in a simplicial complex associated with the splitting surface arising from the Heegard decompositions of the 3-manifold. We prove that the splitting distances in each case is bounded from below under stabilizations and as a result the associated invariants converge to a non-trivial limit under stabilizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimating distances in simplicial complexes with applications to 3-manifolds and handlebody-knots Mondal, Sayantika Pongtanapaisan, Puttipong Vo, Hanh Geometric Topology 57M25 We study distance relations in various simplicial complexes associated with low-dimensional manifolds. In particular, complexes satisfying certain topological conditions with vertices as simple multi-curves. We obtain bounds on the distances in such complexes in terms of number of components in the vertices and distance in the curve complex. We then define new invariants for closed 3-manifolds and handlebody-knots. These are defined using the splitting distance which is calculated using the distance in a simplicial complex associated with the splitting surface arising from the Heegard decompositions of the 3-manifold. We prove that the splitting distances in each case is bounded from below under stabilizations and as a result the associated invariants converge to a non-trivial limit under stabilizations. |
| title | Estimating distances in simplicial complexes with applications to 3-manifolds and handlebody-knots |
| topic | Geometric Topology 57M25 |
| url | https://arxiv.org/abs/2505.00815 |