Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 3005-3027 |
| Number of pages | 23 |
| Journal | Algebraic and Geometric Topology |
| Volume | 16 |
| Issue number | 5 |
| DOIs | |
| State | Published - Nov 7 2016 |
Bibliographical note
Publisher Copyright:© 2016, Mathematical Sciences Publishers. All rights reserved.
Funding
| Funders | Funder number |
|---|---|
| U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China | 1202213 |
Keywords
- Adams spectral sequence
- Eta-inverted stable homotopy group
- Motivic homotopy theory
- Stable homotopy group
ASJC Scopus subject areas
- Geometry and Topology
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