Equivariant Steenrod Operations
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866912865475100672 |
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| author | Bhattacharya, Prasit Waugh, Alex Zeng, Mingcong Zou, Foling |
| author_facet | Bhattacharya, Prasit Waugh, Alex Zeng, Mingcong Zou, Foling |
| contents | We introduce the notion of $\mathrm{R}$-Eulerian sequences for any $\mathcal{N}_\infty$-ring spectrum $\mathrm{R}$ of finite orientation order. We prove that each $\mathrm{R}$-Eulerian sequence determines a stable $\mathrm{R}$-cohomology operation. Furthermore, we show that the collection of $\mathrm{R}$-Eulerian sequences carries a natural additive and a multiplicative structure which is linear over the coefficient ring. As an application, we specialize to equivariant ordinary cohomology with coefficients in finite fields and construct genuine equivariant Steenrod operations for all finite groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant Steenrod Operations Bhattacharya, Prasit Waugh, Alex Zeng, Mingcong Zou, Foling Algebraic Topology 55S91, 55N91, 55P43, 55P92, 55S05, 55P91 We introduce the notion of $\mathrm{R}$-Eulerian sequences for any $\mathcal{N}_\infty$-ring spectrum $\mathrm{R}$ of finite orientation order. We prove that each $\mathrm{R}$-Eulerian sequence determines a stable $\mathrm{R}$-cohomology operation. Furthermore, we show that the collection of $\mathrm{R}$-Eulerian sequences carries a natural additive and a multiplicative structure which is linear over the coefficient ring. As an application, we specialize to equivariant ordinary cohomology with coefficients in finite fields and construct genuine equivariant Steenrod operations for all finite groups. |
| title | Equivariant Steenrod Operations |
| topic | Algebraic Topology 55S91, 55N91, 55P43, 55P92, 55S05, 55P91 |
| url | https://arxiv.org/abs/2511.09816 |