A closed manifold is a fat CW complex
Geometric Topology
2025-01-07 v3 Algebraic Topology
Abstract
The main purpose of this paper is to introduce a new smooth version of a CW complex named a fat CW complex, and to show that it includes all closed manifolds, because existing smooth versions of CW complexes (e.g. [Iwa22]) do not have such property. We also verify that de Rham theorem holds for a fat CW complex and that a regular CW complex is reflexive in the sense of Y. Karshon, J. Watts and P. I-Zemmour. Further, any topological CW complex is topologically homotopy equivalent to a fat CW complex. So, a fat CW complex enjoys many nice properties.
Cite
@article{arxiv.2309.07379,
title = {A closed manifold is a fat CW complex},
author = {Norio Iwase and Yuki Kojima},
journal= {arXiv preprint arXiv:2309.07379},
year = {2025}
}
Comments
16 pages