C_2-Equivariant Stable Stems

Abstract

We compute the 2-primary $C_2$-equivariant stable homotopy groups $\pi^{C_2}_{s,c}$ 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 $\pi^{C_2}_{s,c} \rightarrow \pi^{\mathrm{cl}}_s$ to the classical stable homotopy groups in the same range.