The $C_2$-equivariant $K(1)$-local sphere

TL;DR

This paper computes the $RO(C_2)$-graded Green functor for the $K(1)$-local sphere at the prime 2, providing detailed algebraic invariants in equivariant stable homotopy theory.

Contribution

It offers the first explicit computation of the $RO(C_2)$-graded Green functor for the $K(1)$-local sphere, advancing understanding in equivariant chromatic homotopy theory.

Findings

Explicit description of the $RO(C_2)$-graded Green functor

New computational techniques for equivariant stable homotopy groups

Enhanced understanding of $C_2$-equivariant $K(1)$-local phenomena

Abstract

We compute the $RO(C_2)$-graded Green functor $\underline{\pi}_\star L_{KU_{C_2}/(2)}S_{C_2}$.