ℤ/2-equivariant and ℝ-motivic stable stems

Abstract

We establish an isomorphism between the stable homotopy groups π ^ s , w R \hat {\pi }^{\mathbb {R}}_{s,w} of the 2-completed R \mathbb {R} -motivic sphere spectrum and the stable homotopy groups π ^ s , w Z / 2 \hat {\pi }^{\mathbb {Z}/2}_{s,w} of the 2-completed Z / 2 \mathbb {Z}/2 -equivariant sphere spectrum, valid in the range s ≥ 3 w − 5 s \geq 3 w - 5 or s ≤ − 1 s \leq -1 .