Filling links and spines in 3-manifolds
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866911982984101888 |
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| author | Freedman, Michael Krushkal, Vyacheslav Leininger, Christopher J. Reid, Alan W. |
| author_facet | Freedman, Michael Krushkal, Vyacheslav Leininger, Christopher J. Reid, Alan W. |
| contents | We introduce and study the notion of filling links in 3-manifolds: a link L is filling in M if for any 1-spine G of M which is disjoint from L, $π_1(G)$ injects into $π_1(M\smallsetminus L)$. A weaker "k-filling" version concerns injectivity modulo k-th term of the lower central series. For each k>1 we construct a k-filling link in the 3-torus. The proof relies on an extension of the Stallings theorem which may be of independent interest. We discuss notions related to "filling" links in 3-manifolds, and formulate several open problems. The appendix by C. Leininger and A. Reid establishes the existence of a filling hyperbolic link in any closed orientable 3-manifold with $π_1(M)$ of rank 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_15644 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Filling links and spines in 3-manifolds Freedman, Michael Krushkal, Vyacheslav Leininger, Christopher J. Reid, Alan W. Geometric Topology We introduce and study the notion of filling links in 3-manifolds: a link L is filling in M if for any 1-spine G of M which is disjoint from L, $π_1(G)$ injects into $π_1(M\smallsetminus L)$. A weaker "k-filling" version concerns injectivity modulo k-th term of the lower central series. For each k>1 we construct a k-filling link in the 3-torus. The proof relies on an extension of the Stallings theorem which may be of independent interest. We discuss notions related to "filling" links in 3-manifolds, and formulate several open problems. The appendix by C. Leininger and A. Reid establishes the existence of a filling hyperbolic link in any closed orientable 3-manifold with $π_1(M)$ of rank 2. |
| title | Filling links and spines in 3-manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2010.15644 |