R-motivic stable stems

Abstract

We compute some R-motivic stable homotopy groups. For $s-w\le 11$, we describe the motivic stable homotopy groups ${\pi }_{s,w}$ of a completion of the R-motivic sphere spectrum. We apply the $\rho$-Bockstein spectral sequence to obtain R-motivic Ext groups from the C-motivic Ext groups, which are well-understood in a large range. These Ext groups are the input to the R-motivic Adams spectral sequence. We fully analyze the Adams differentials in a range, and we also analyze hidden extensions by $\rho$, 2, and $\eta$. As a consequence of our computations, we recover Mahowald invariants of many low-dimensional classical stable homotopy elements.

Cited by in corpus (1)

• C_2-equivariant and R-motivic stable stems, II