Realizability of hypergraphs and intrinsic link theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2014
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| _version_ | 1866911357062873088 |
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| author | Skopenkov, Arkadiy |
| author_facet | Skopenkov, Arkadiy |
| contents | In this expository paper we present short simple proofs of Conway-Gordon-Sachs' theorem on intrinsic linking in three-dimensional space, as well as van Kampen-Flores' and Ummel's theorems on intrinsic intersections. The latter are related to nonrealizability of certain hypergraphs in four-dimensional space. The proofs use a reduction to lower dimensions which allows to exhibit relation between these results. We use elementary language which allows to present the main ideas without technicalities. Thus our exposition is accessible to non-specialists in the area, including students who know basic three-dimensional geometry, and who are ready to learn straightforward four-dimensional generalizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1402_0658 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Realizability of hypergraphs and intrinsic link theory Skopenkov, Arkadiy Metric Geometry Geometric Topology 05C65, 52C35, 57Q35, 57M15 In this expository paper we present short simple proofs of Conway-Gordon-Sachs' theorem on intrinsic linking in three-dimensional space, as well as van Kampen-Flores' and Ummel's theorems on intrinsic intersections. The latter are related to nonrealizability of certain hypergraphs in four-dimensional space. The proofs use a reduction to lower dimensions which allows to exhibit relation between these results. We use elementary language which allows to present the main ideas without technicalities. Thus our exposition is accessible to non-specialists in the area, including students who know basic three-dimensional geometry, and who are ready to learn straightforward four-dimensional generalizations. |
| title | Realizability of hypergraphs and intrinsic link theory |
| topic | Metric Geometry Geometric Topology 05C65, 52C35, 57Q35, 57M15 |
| url | https://arxiv.org/abs/1402.0658 |