Topological lower bounds on the sizes of simplicial complexes and simplicial sets

Sergey Avvakumov; Roman Karasev

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arXiv · 2110.03556

Topological lower bounds on the sizes of simplicial complexes and simplicial sets

Sergey Avvakumov·Roman Karasev

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Abstract

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 $(S^1)^n$.

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BibTeX RIS

Sergey Avvakumov, Roman Karasev. 2021-10-07. Topological lower bounds on the sizes of simplicial complexes and simplicial sets. https://arxiv.org/abs/2110.03556

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