The η–inverted ℝ–motivic sphere
Algebraic and Geometric Topology
We use an Adams spectral sequence to calculate the R-motivic stable homotopy groups after inverting eta. The first step is to apply a Bockstein spectral sequence in order to obtain h_1-inverted R-motivic Ext groups, which serve as the input to the eta-inverted R-motivic Adams spectral sequence. The second step is to analyze Adams differentials. The final answer is that the Milnor-Witt (4k-1)-stem has order 2^u+1, where u is the 2-adic valuation of 4k. This answer is reminiscent of the classical
... image of J. We also explore some of the Toda bracket structure of the eta-inverted R-motivic stable homotopy groups.