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We use the $C_2$-equivariant Adams spectral sequence to compute part of the$C_2$-equivariant stable homotopy groups $\pi^{C_2}_{n,n}$. This allows us torecover results of Bredon and Landweber on the image of the geometricfixed-points map from the equivariant homotopy group $\pi^{C_2}_{n,n}$ to theclassical $\pi_0$. We also recover results of Mahowald and Ravenel on theMahowald root invariants of the elements $2^k$.

The Bredon-Landweber region in $C_2$-equivariant stable homotopy groups