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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2503.13748 |
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| _version_ | 1866908273040424960 |
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| author | Minami, Haruo |
| author_facet | Minami, Haruo |
| contents | We consider a compact Lie group as a framed manifold equipped with the left invarianat framing $\mathscr{L}$. In a previous paper we have proved that the Adams $e_\mathbb{C}$-invariant value of $SU(2n)$ $(n\ge 2)$ gives a generator of the image of $e_\mathbb{C}$ by twisting $\mathscr{L}$ by a certain map. In this note we show that in a similar way we can obtain analogous results for $Sp(4n+1)$ and $Spin(8n-2)$ $(n\ge 1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13748 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The groups $Sp(4n+1)$ and $Spin(8n-2)$ as framed manifolds Minami, Haruo Algebraic Topology 22E46, 55Q45 We consider a compact Lie group as a framed manifold equipped with the left invarianat framing $\mathscr{L}$. In a previous paper we have proved that the Adams $e_\mathbb{C}$-invariant value of $SU(2n)$ $(n\ge 2)$ gives a generator of the image of $e_\mathbb{C}$ by twisting $\mathscr{L}$ by a certain map. In this note we show that in a similar way we can obtain analogous results for $Sp(4n+1)$ and $Spin(8n-2)$ $(n\ge 1)$. |
| title | The groups $Sp(4n+1)$ and $Spin(8n-2)$ as framed manifolds |
| topic | Algebraic Topology 22E46, 55Q45 |
| url | https://arxiv.org/abs/2503.13748 |