The eta-inverted R-motivic sphere
Abstract
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.
Keywords
Cite
@article{arxiv.1510.01283,
title = {The eta-inverted R-motivic sphere},
author = {Bertrand J. Guillou and Daniel C. Isaksen},
journal= {arXiv preprint arXiv:1510.01283},
year = {2016}
}
Comments
18 pages. Minor correction to statement of Theorem 6.2. Descriptions "h_1-local" and "eta-local" replaced with "h_1-inverted" and "eta-inverted", including in the title