C_2-Equivariant Stable Stems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917647730343936 |
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| author | Guillou, Bertrand J. Isaksen, Daniel C. |
| author_facet | Guillou, Bertrand J. Isaksen, Daniel C. |
| contents | We compute the 2-primary $C_2$-equivariant stable homotopy groups $π^{C_2}_{s,c}$ for stems between 0 and 25 (i.e., $0 \leq s \leq 25$) and for coweights between -1 and 7 (i.e., $-1 \leq c \leq 7)$. Our results, combined with periodicity isomorphisms and sufficiently extensive $\mathbb{R}$-motivic computations, would determine all of the $C_2$-equivariant stable homotopy groups for all stems up to 20. We also compute the forgetful map $π^{C_2}_{s,c} \rightarrow π^{\mathrm{cl}}_s$ to the classical stable homotopy groups in the same range. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_14627 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | C_2-Equivariant Stable Stems Guillou, Bertrand J. Isaksen, Daniel C. Algebraic Topology 55Q91, 55T15, 55Q45 We compute the 2-primary $C_2$-equivariant stable homotopy groups $π^{C_2}_{s,c}$ for stems between 0 and 25 (i.e., $0 \leq s \leq 25$) and for coweights between -1 and 7 (i.e., $-1 \leq c \leq 7)$. Our results, combined with periodicity isomorphisms and sufficiently extensive $\mathbb{R}$-motivic computations, would determine all of the $C_2$-equivariant stable homotopy groups for all stems up to 20. We also compute the forgetful map $π^{C_2}_{s,c} \rightarrow π^{\mathrm{cl}}_s$ to the classical stable homotopy groups in the same range. |
| title | C_2-Equivariant Stable Stems |
| topic | Algebraic Topology 55Q91, 55T15, 55Q45 |
| url | https://arxiv.org/abs/2404.14627 |