We use an Adams spectral sequence to calculate the ℝ-motivic stable homotopy groups after inverting η. The first step is to apply a Bockstein spectral sequence in order to obtain h1-inverted ℝ-motivic Ext groups, which serve as the input to the η-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 2u+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 η-inverted ℝ-motivic stable homotopy groups.
|Number of pages||23|
|Journal||Algebraic and Geometric Topology|
|State||Published - Nov 7 2016|
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- Adams spectral sequence
- Eta-inverted stable homotopy group
- Motivic homotopy theory
- Stable homotopy group
ASJC Scopus subject areas
- Geometry and Topology