The η-inverted ℝ-motivic sphere

Bertrand J. Guillou, Daniel C. Isaksen

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 languageEnglish
Pages (from-to)3005-3027
Number of pages23
JournalAlgebraic and Geometric Topology
Issue number5
StatePublished - Nov 7 2016

Bibliographical note

Publisher Copyright:
© 2016, Mathematical Sciences Publishers. All rights reserved.


  • 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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