On spherical fibrations and Poincare complexes
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913764793647104 |
|---|---|
| author | Shen, Wen |
| author_facet | Shen, Wen |
| contents | In this paper, we prove that certain spherical fibrations over certain CW-complexes are stably fibre homotopy equivalent to $\mm{TOP}$-spherical fibrations (see Definition 1,1). Applying this result, we get a sufficient condition for whether a Poincar$\mm{\acute{e}}$ complex is of the homotopy type of a topological manifold. Moreover, we present the classification for some highly connected manifolds by the homotopy types of highly connected Poincar$\mm{\acute{e}}$ complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16019 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On spherical fibrations and Poincare complexes Shen, Wen Geometric Topology Algebraic Topology In this paper, we prove that certain spherical fibrations over certain CW-complexes are stably fibre homotopy equivalent to $\mm{TOP}$-spherical fibrations (see Definition 1,1). Applying this result, we get a sufficient condition for whether a Poincar$\mm{\acute{e}}$ complex is of the homotopy type of a topological manifold. Moreover, we present the classification for some highly connected manifolds by the homotopy types of highly connected Poincar$\mm{\acute{e}}$ complexes. |
| title | On spherical fibrations and Poincare complexes |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2406.16019 |