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

TL;DR

This paper employs the $C_2$-equivariant Adams spectral sequence to compute parts of the $C_2$-equivariant stable homotopy groups, recovering classical results on fixed points and root invariants.

Contribution

It introduces a method to compute equivariant homotopy groups and recovers classical results on fixed points and root invariants within this framework.

Findings

Computed parts of $C_2$-equivariant stable homotopy groups.

Reproduced classical results of Bredon and Landweber on fixed points.

Confirmed Mahowald and Ravenel's results on root invariants.

Abstract

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 to recover results of Bredon and Landweber on the image of the geometric fixed-points map from the equivariant homotopy group $\pi^{C_2}_{n,n}$ to the classical $\pi_0$. We also recover results of Mahowald and Ravenel on the Mahowald root invariants of the elements $2^k$.