A closed manifold is a fat CW complex
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915090943442944 |
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| author | Iwase, Norio Kojima, Yuki |
| author_facet | Iwase, Norio Kojima, Yuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07379 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A closed manifold is a fat CW complex Iwase, Norio Kojima, Yuki Geometric Topology Algebraic Topology Primary 58A05, Secondary 57R35, 57R55, 58A40 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. |
| title | A closed manifold is a fat CW complex |
| topic | Geometric Topology Algebraic Topology Primary 58A05, Secondary 57R35, 57R55, 58A40 |
| url | https://arxiv.org/abs/2309.07379 |