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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2412.16055 |
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| _version_ | 1866912183954178048 |
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| author | Holmsen, Andreas F. McCourt, Grace McGinnis, Daniel Zerbib, Shira |
| author_facet | Holmsen, Andreas F. McCourt, Grace McGinnis, Daniel Zerbib, Shira |
| contents | We prove a generalization of the topological Tverberg theorem. One special instance of our general theorem is the following: Let $Δ$ denote the 8-dimensional simplex viewed as an abstract simplicial complex, and suppose that its vertices are arranged in a $3\times 3$ array. Then for any continuous map $f:Δ\to \mathbb{R}^3$ it is possible to partition the rows or the columns of the vertex array into two parts, such that the disjoint faces $σ$ and $τ$ induced by the two parts satisfy $f(σ)\cap f(τ) \neq \emptyset$. Our result also has consequences for geometric transversals and topological Helly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A topological product Tverberg Theorem Holmsen, Andreas F. McCourt, Grace McGinnis, Daniel Zerbib, Shira Combinatorics We prove a generalization of the topological Tverberg theorem. One special instance of our general theorem is the following: Let $Δ$ denote the 8-dimensional simplex viewed as an abstract simplicial complex, and suppose that its vertices are arranged in a $3\times 3$ array. Then for any continuous map $f:Δ\to \mathbb{R}^3$ it is possible to partition the rows or the columns of the vertex array into two parts, such that the disjoint faces $σ$ and $τ$ induced by the two parts satisfy $f(σ)\cap f(τ) \neq \emptyset$. Our result also has consequences for geometric transversals and topological Helly. |
| title | A topological product Tverberg Theorem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.16055 |