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This article computes some motivic stable homotopy groups over R. For 0 <= p - q <= 3, we describe the motivic stable homotopy groups of a completion of the motivic sphere spectrum. These are the first four Milnor-Witt stems. We start with the known Ext groups over C and apply the rho-Bockstein spectral sequence to obtain Ext groups over R. This is the input to an Adams spectral sequence, which collapses in our low dimensional range.
We compute some R-motivic stable homotopy groups. For $s - w leq 11$, 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 g
We show that the $C_2$-equivariant and $mathbb{R}$-motivic stable homotopy groups are isomorphic in a range. This result supersedes previous work of Dugger and the third author.
We compute the stable homotopy groups up to dimension 90, except for some carefully enumerated uncertainties.
In this paper, we study {bf twisted Milnor hypersurfaces} and compute their $hat A$-genus and Atiyah-Singer-Milnor $alpha$-invariant. Our tool to compute the $alpha$-invariant is Zhangs analytic Rokhlin congruence formula. We also give some applicati