The $\mathbb Z/p$-equivariant cohomology of genus zero Deligne-Mumford space with $1+p$ marked points
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909886150868992 |
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| author | Kim, Dain Wilkins, Nicholas |
| author_facet | Kim, Dain Wilkins, Nicholas |
| contents | We prove that the Serre spectral sequence of the fibration $\overline{\mathcal M}_{0, 1+p} \to E\mathbb Z/p \times_{\mathbb Z/p} \overline{\mathcal M}_{0, 1+p} \to B \mathbb Z/p$ collapses at the $E_2$ page. We use this to prove that: for any element of the $\mathbb Z/p$-equivariant cohomology with $\mathbb F_p$-coefficients of genus zero Deligne-Mumford space with $1+p$ marked points, if this element is torsion then it is non-equivariant. This concludes that the only "interesting" $\mathbb Z/p$-equivariant operations are quantum Steenrod power operations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06618 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The $\mathbb Z/p$-equivariant cohomology of genus zero Deligne-Mumford space with $1+p$ marked points Kim, Dain Wilkins, Nicholas Algebraic Topology Algebraic Geometry Symplectic Geometry 55N91, 55N25, 55T10, 53D45 We prove that the Serre spectral sequence of the fibration $\overline{\mathcal M}_{0, 1+p} \to E\mathbb Z/p \times_{\mathbb Z/p} \overline{\mathcal M}_{0, 1+p} \to B \mathbb Z/p$ collapses at the $E_2$ page. We use this to prove that: for any element of the $\mathbb Z/p$-equivariant cohomology with $\mathbb F_p$-coefficients of genus zero Deligne-Mumford space with $1+p$ marked points, if this element is torsion then it is non-equivariant. This concludes that the only "interesting" $\mathbb Z/p$-equivariant operations are quantum Steenrod power operations. |
| title | The $\mathbb Z/p$-equivariant cohomology of genus zero Deligne-Mumford space with $1+p$ marked points |
| topic | Algebraic Topology Algebraic Geometry Symplectic Geometry 55N91, 55N25, 55T10, 53D45 |
| url | https://arxiv.org/abs/2212.06618 |