Some `converses' to intrinsic linking theorems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866915711546294272 |
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| author | Karasev, R. Skopenkov, A. |
| author_facet | Karasev, R. Skopenkov, A. |
| contents | A low-dimensional version of our main result is the following `converse' of the Conway-Gordon-Sachs Theorem on intrinsic linking of the graph $K_6$ in 3-space:
For any integer $z$ there are 6 points $1,2,3,4,5,6$ in 3-space, of which every two $i,j$ are joined by a polygonal line $ij$, the interior of one polygonal line is disjoint with any other polygonal line, the linking coefficient of any pair of disjoint 3-cycles except for $\{123,456\}$ is zero, and for the exceptional pair $\{123,456\}$ is $2z+1$.
We prove a higher-dimensional analogue, which is a `converse' of a lemma by Segal-Spież. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_02523 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Some `converses' to intrinsic linking theorems Karasev, R. Skopenkov, A. Geometric Topology Computational Geometry Algebraic Topology 57Q35, 57K45, 55S91, 68U05 A low-dimensional version of our main result is the following `converse' of the Conway-Gordon-Sachs Theorem on intrinsic linking of the graph $K_6$ in 3-space: For any integer $z$ there are 6 points $1,2,3,4,5,6$ in 3-space, of which every two $i,j$ are joined by a polygonal line $ij$, the interior of one polygonal line is disjoint with any other polygonal line, the linking coefficient of any pair of disjoint 3-cycles except for $\{123,456\}$ is zero, and for the exceptional pair $\{123,456\}$ is $2z+1$. We prove a higher-dimensional analogue, which is a `converse' of a lemma by Segal-Spież. |
| title | Some `converses' to intrinsic linking theorems |
| topic | Geometric Topology Computational Geometry Algebraic Topology 57Q35, 57K45, 55S91, 68U05 |
| url | https://arxiv.org/abs/2008.02523 |