Stable Adams operations on $RO(C_2)$-graded homotopy groups

Abstract

The $C_2$-spectrum of Atiyah's Real $K$-theory is denoted by $\mathbf{KR}$ and the $C_2$-spectrum of topological modular forms of level structure ${\Gamma }_1(3)$ by ${\mathbf{TMF}}_1(3)$. In this short note we compute the $C_2$-equivariant stable Adams operations on the $RO(C_2)$-graded homotopy groups of $\mathbf{KR}$ and ${\mathbf{TMF}}_1(3)$.

arXiv comment10 pages; to appear in Homology, Homotopy and Applications