Topological Complexity and Finite Domination

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 $M$.

arXiv comment15 pages