On manifolds homeomorphic to spheres
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908543187156992 |
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| author | Basu, Somnath Prasad, Sachchidanand |
| author_facet | Basu, Somnath Prasad, Sachchidanand |
| contents | We prove a result analogous to Reeb's theorem in the context of Morse-Bott functions: if a closed, smooth manifold $M$ admits a Morse-Bott function having two critical submanifolds $S^k$ and $S^l$ ($k \neq l$), then $M$ has dimension $k+l+1$ and is homeomorphic to the standard sphere $S^{k+l+1}$ but not necessarily diffeomorphic to it. We also prove similar results for projective spaces over the real numbers, complex numbers and quaternions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13008 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On manifolds homeomorphic to spheres Basu, Somnath Prasad, Sachchidanand Differential Geometry Algebraic Topology Geometric Topology Primary: 57R70, 55M99, 55Q40, Secondary: 55R10 We prove a result analogous to Reeb's theorem in the context of Morse-Bott functions: if a closed, smooth manifold $M$ admits a Morse-Bott function having two critical submanifolds $S^k$ and $S^l$ ($k \neq l$), then $M$ has dimension $k+l+1$ and is homeomorphic to the standard sphere $S^{k+l+1}$ but not necessarily diffeomorphic to it. We also prove similar results for projective spaces over the real numbers, complex numbers and quaternions. |
| title | On manifolds homeomorphic to spheres |
| topic | Differential Geometry Algebraic Topology Geometric Topology Primary: 57R70, 55M99, 55Q40, Secondary: 55R10 |
| url | https://arxiv.org/abs/2509.13008 |