Topological Complexity and Finite Domination

Lizhi Chen

Topological Complexity and Finite Domination

Geometric Topology 2026-06-29 v1 Differential Geometry

Authors: Lizhi Chen

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 $M$ .

Cite

@article{arxiv.2606.29730,
  title  = {Topological Complexity and Finite Domination},
  author = {Lizhi Chen},
  journal= {arXiv preprint arXiv:2606.29730},
  year   = {2026}
}

Comments

15 pages