The $H \underline{\mathbb{F}}_2$-homology of $C_2$-equivariant Eilenberg-MacLane spaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910760099119104 |
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| author | Petersen, Sarah |
| author_facet | Petersen, Sarah |
| contents | We extend Ravenel-Wilson Hopf ring techniques to $C_2$-equivariant homotopy theory. Our main application and motivation is a computation of the $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacLane spaces. The result we obtain for $C_2$-equivariant Eilenberg-MacLane spaces associated to the constant Mackey functor $\underline{\mathbb{F}}_2$ gives a $C_2$-equivariant analogue of the classical computation due to Serre. We also investigate a twisted bar spectral sequence computing the homology of these equivariant Eilenberg-MacLane spaces and suggest the existence of another twisted bar spectral sequence with $E^2$-page given in terms of a twisted Tor functor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_08165 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The $H \underline{\mathbb{F}}_2$-homology of $C_2$-equivariant Eilenberg-MacLane spaces Petersen, Sarah Algebraic Topology 55P91 (Primary) 55P20, 55N91 (Secondary) We extend Ravenel-Wilson Hopf ring techniques to $C_2$-equivariant homotopy theory. Our main application and motivation is a computation of the $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-MacLane spaces. The result we obtain for $C_2$-equivariant Eilenberg-MacLane spaces associated to the constant Mackey functor $\underline{\mathbb{F}}_2$ gives a $C_2$-equivariant analogue of the classical computation due to Serre. We also investigate a twisted bar spectral sequence computing the homology of these equivariant Eilenberg-MacLane spaces and suggest the existence of another twisted bar spectral sequence with $E^2$-page given in terms of a twisted Tor functor. |
| title | The $H \underline{\mathbb{F}}_2$-homology of $C_2$-equivariant Eilenberg-MacLane spaces |
| topic | Algebraic Topology 55P91 (Primary) 55P20, 55N91 (Secondary) |
| url | https://arxiv.org/abs/2206.08165 |