The $RO(\mathcal{K})$-graded Coefficients of $H\underline{A}$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910902346842112 |
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| author | Keyes, Jesse |
| author_facet | Keyes, Jesse |
| contents | In $G$-equivariant stable homotopy theory, it is known that the equivariant Eilenberg-Mac Lane spectra representing ordinary equivariant cohomology have nontrivial $RO(G)$-graded homotopy corresponding to the equivariant (co)homology of representation spheres. We will compute the universal case of this ordinary $RO(G)$-graded homotopy in the case of $G=\mathcal{K}$, where $\mathcal{K}$ is the Klein-four group. In particular, we will compute a subring of the $RO(\mathcal{K})$-graded homotopy of $H\underline{A}$ for $\underline{A}$ the Burnside Mackey functor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $RO(\mathcal{K})$-graded Coefficients of $H\underline{A}$ Keyes, Jesse Algebraic Topology In $G$-equivariant stable homotopy theory, it is known that the equivariant Eilenberg-Mac Lane spectra representing ordinary equivariant cohomology have nontrivial $RO(G)$-graded homotopy corresponding to the equivariant (co)homology of representation spheres. We will compute the universal case of this ordinary $RO(G)$-graded homotopy in the case of $G=\mathcal{K}$, where $\mathcal{K}$ is the Klein-four group. In particular, we will compute a subring of the $RO(\mathcal{K})$-graded homotopy of $H\underline{A}$ for $\underline{A}$ the Burnside Mackey functor. |
| title | The $RO(\mathcal{K})$-graded Coefficients of $H\underline{A}$ |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2503.03173 |