Cohomology of the diffeomorphism group of the connected sum of two generic lens spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910747376746496 |
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| author | Lelkes, Zoltán |
| author_facet | Lelkes, Zoltán |
| contents | We consider the connected sum of two three-dimensional lens spaces $L_1\#L_2$, where $L_1$ and $L_2$ are non-diffeomorphic and are of a certain "generic" type. Our main result is the calculation of the cohomology ring $H^\ast(B\text{Diff}(L_1\#L_2);\mathbb{Q})$, where $\text{Diff}(L_1\#L_2)$ is the diffeomorphism group of $M$ equipped with the $C^\infty$-topology. We know the homotopy type of the diffeomorphism groups of generic lens spaces this, combined with a theorem of Hatcher forms the basis of our argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11225 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomology of the diffeomorphism group of the connected sum of two generic lens spaces Lelkes, Zoltán Geometric Topology We consider the connected sum of two three-dimensional lens spaces $L_1\#L_2$, where $L_1$ and $L_2$ are non-diffeomorphic and are of a certain "generic" type. Our main result is the calculation of the cohomology ring $H^\ast(B\text{Diff}(L_1\#L_2);\mathbb{Q})$, where $\text{Diff}(L_1\#L_2)$ is the diffeomorphism group of $M$ equipped with the $C^\infty$-topology. We know the homotopy type of the diffeomorphism groups of generic lens spaces this, combined with a theorem of Hatcher forms the basis of our argument. |
| title | Cohomology of the diffeomorphism group of the connected sum of two generic lens spaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2412.11225 |