Topological lower bounds on the sizes of simplicial complexes and simplicial sets
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916347217182720 |
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| author | Avvakumov, Sergey Karasev, Roman |
| author_facet | Avvakumov, Sergey Karasev, Roman |
| contents | We prove that if an $n$-dimensional space $X$ satisfies certain topological conditions then any triangulation of $X$ as well as any its representation as a simplicial set with contractible faces has at least $2^n$ faces of dimension $n$.
One example of such $X$ is the $n$-dimensional torus $(S^1)^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_03556 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Topological lower bounds on the sizes of simplicial complexes and simplicial sets Avvakumov, Sergey Karasev, Roman Algebraic Topology Combinatorics 55U10, 05E45 We prove that if an $n$-dimensional space $X$ satisfies certain topological conditions then any triangulation of $X$ as well as any its representation as a simplicial set with contractible faces has at least $2^n$ faces of dimension $n$. One example of such $X$ is the $n$-dimensional torus $(S^1)^n$. |
| title | Topological lower bounds on the sizes of simplicial complexes and simplicial sets |
| topic | Algebraic Topology Combinatorics 55U10, 05E45 |
| url | https://arxiv.org/abs/2110.03556 |