C_2-Equivariant Stable Stems

Abstract

We compute the 2-primary $C_2$-equivariant stable homotopy groups $\ddot{I}{€}_{s,c}^{C_2}$ for stems between 0 and 25 (i.e., $0\le s\le 25$) and for coweights between -1 and 7 (i.e., $-1\le c\le 7)$. 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 $\ddot{I}{€}_{s,c}^{C_2}\to \ddot{I}{€}_s^{\mathrm{cl}}$ to the classical stable homotopy groups in the same range.

109 pages, including 42 pages of charts. Comments welcome!