The $RO(C_4)$ cohomology of the infinite real projective space
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866911813535268864 |
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| author | Georgakopoulos, Nick |
| author_facet | Georgakopoulos, Nick |
| contents | Following the Hu-Kriz method of computing the $C_2$ genuine dual Steenrod algebra $(H\mathbf F_2)_{\bigstar}(H\mathbf F_2)$, we calculate the $C_4$ equivariant Bredon cohomology of the classifying space $\mathbf R P^{\infty ρ}=B_{C_4}Σ_{2}$ as an $RO(C_4)$ graded Green-functor. We prove that as a module over the homology of a point (which we also compute), this cohomology is not flat. As a result, it can't be used as a test module for obtaining generators in $(H\mathbf F_2)_{\bigstar}(H\mathbf F_2)$ as Hu-Kriz do in the $C_2$ case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_11407 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The $RO(C_4)$ cohomology of the infinite real projective space Georgakopoulos, Nick Algebraic Topology 55N91, 55P91 Following the Hu-Kriz method of computing the $C_2$ genuine dual Steenrod algebra $(H\mathbf F_2)_{\bigstar}(H\mathbf F_2)$, we calculate the $C_4$ equivariant Bredon cohomology of the classifying space $\mathbf R P^{\infty ρ}=B_{C_4}Σ_{2}$ as an $RO(C_4)$ graded Green-functor. We prove that as a module over the homology of a point (which we also compute), this cohomology is not flat. As a result, it can't be used as a test module for obtaining generators in $(H\mathbf F_2)_{\bigstar}(H\mathbf F_2)$ as Hu-Kriz do in the $C_2$ case. |
| title | The $RO(C_4)$ cohomology of the infinite real projective space |
| topic | Algebraic Topology 55N91, 55P91 |
| url | https://arxiv.org/abs/2104.11407 |