$C$-triviality of manifolds of low dimensions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911554518122496 |
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| author | Sharma, Shubham Renanse, Animesh |
| author_facet | Sharma, Shubham Renanse, Animesh |
| contents | A space $X$ is said to be $C$-trivial if the total Chern class $c(α)$ equals $1$ for every complex vector bundle $α$ over $X$. In this note we give a complete homological classification of $C$-trivial closed smooth manifolds of dimension $< 7$. In dimension $7$ we give a complete classification of orientable $C$-trivial manifolds and in the non-orientable case we give necessary homological conditions for the manifold to be $C$-trivial. Our main tool is the Atiyah-Hirzebruch spectral sequence and orders of its differentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05558 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $C$-triviality of manifolds of low dimensions Sharma, Shubham Renanse, Animesh Algebraic Topology 57R20 A space $X$ is said to be $C$-trivial if the total Chern class $c(α)$ equals $1$ for every complex vector bundle $α$ over $X$. In this note we give a complete homological classification of $C$-trivial closed smooth manifolds of dimension $< 7$. In dimension $7$ we give a complete classification of orientable $C$-trivial manifolds and in the non-orientable case we give necessary homological conditions for the manifold to be $C$-trivial. Our main tool is the Atiyah-Hirzebruch spectral sequence and orders of its differentials. |
| title | $C$-triviality of manifolds of low dimensions |
| topic | Algebraic Topology 57R20 |
| url | https://arxiv.org/abs/2411.05558 |