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R$\mathbb {R}$-motivic stable stems
Journal of Topology ( IF 1.1 ) Pub Date : 2022-07-27 , DOI: 10.1112/topo.12256
Eva Belmont 1 , Daniel C. Isaksen 2
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We compute some R$\mathbb {R}$-motivic stable homotopy groups. For s−w⩽11$s - w \leqslant 11$, we describe the motivic stable homotopy groups πs,w$\pi _{s,w}$ of a completion of the R$\mathbb {R}$-motivic sphere spectrum. We apply the ρ$\rho$-Bockstein spectral sequence to obtain R$\mathbb {R}$-motivic Ext$\operatorname{Ext}$ groups from the C$\mathbb {C}$-motivic Ext$\operatorname{Ext}$ groups, which are well understood in a large range. These Ext$\operatorname{Ext}$ groups are the input to the R$\mathbb {R}$-motivic Adams spectral sequence. We fully analyze the Adams differentials in a range, and we also analyze hidden extensions by ρ$\rho$, 2, and η$\eta$. As a consequence of our computations, we recover Mahowald invariants of many low-dimensional classical stable homotopy elements.
更新日期：2022-07-28
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