抄録
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., that of Iwase (Kyushu J. Math. 76(1) (2022),
177–186), do not have such a property. We also verify that the de Rham theorem holds for
a fat CW complex and that a regular CW complex is reflexive in the sense of Batubenge,
Iglesias-Zemmour, Karshon, and Watts (Rocky Mountain J. Math. To appear). Further, any
topological CW complex is topologically homotopy equivalent to a fat CW complex. So, a fat
CW complex enjoys many nice properties.
