Linear actions of $\mathbb{Z}/p\times\mathbb{Z}/p$ on $S^{2n-1}\times S^{2n-1}$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914694964445184 |
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| author | Fowler, Jim Thatcher, Courtney |
| author_facet | Fowler, Jim Thatcher, Courtney |
| contents | For an odd prime $p$, we consider free actions of $(\mathbb{Z}/p)^2$ on $S^{2n-1}\times S^{2n-1}$ given by linear actions of $(\mathbb{Z}/p)^2$ on $\mathbb{R}^{4n}$. Simple examples include a lens space cross a lens space, but $k$-invariant calculations show that other quotients exist. Using the tools of Postnikov towers and surgery theory, the quotients are classified up to homotopy by the $k$-invariants and up to homeomorphism by the Pontrjagin classes. We will present these results and demonstrate how to calculate the $k$-invariants and the Pontrjagin classes from the rotation numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_11257 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Linear actions of $\mathbb{Z}/p\times\mathbb{Z}/p$ on $S^{2n-1}\times S^{2n-1}$ Fowler, Jim Thatcher, Courtney Geometric Topology 57R65 For an odd prime $p$, we consider free actions of $(\mathbb{Z}/p)^2$ on $S^{2n-1}\times S^{2n-1}$ given by linear actions of $(\mathbb{Z}/p)^2$ on $\mathbb{R}^{4n}$. Simple examples include a lens space cross a lens space, but $k$-invariant calculations show that other quotients exist. Using the tools of Postnikov towers and surgery theory, the quotients are classified up to homotopy by the $k$-invariants and up to homeomorphism by the Pontrjagin classes. We will present these results and demonstrate how to calculate the $k$-invariants and the Pontrjagin classes from the rotation numbers. |
| title | Linear actions of $\mathbb{Z}/p\times\mathbb{Z}/p$ on $S^{2n-1}\times S^{2n-1}$ |
| topic | Geometric Topology 57R65 |
| url | https://arxiv.org/abs/2209.11257 |