The Bredon-Landweber Region in $C_2$-Equivariant Stable Homotopy Groups

Abstract

We use the $C_2$-equivariant Adams spectral sequence to compute part of the $C_2$-equivariant stable homotopy groups ${\pi }_{n,n}^{C_2}$. This allows us to recover results of Bredon and Landweber on the image of the geometric fixed-points map ${\pi }_{n,n}^{C_2}\to {\pi }_0$. We also recover results of Mahowald and Ravenel on the Mahowald root invariants of the elements $2^k$.