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arXiv · 2606.29730

Topological Complexity and Finite Domination

Lizhi Chen
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Abstract

Let $M$ be a closed, connected, smooth $n$-dimensional manifold. We prove that $M$ is dominated by the underlying space of the $n$-skeleton of a finite simplicial complex. Furthermore, the total number of simplices in the $n$-skeleton is bounded above by a constant depending only on $n$ and the embolic volume of $M$.

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Lizhi Chen. 2026-06-29. Topological Complexity and Finite Domination. https://arxiv.org/abs/2606.29730

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