English

R-motivic stable stems

Algebraic Topology 2020-01-13 v1

Abstract

We compute some R-motivic stable homotopy groups. For sw11s - w \leq 11, we describe the motivic stable homotopy groups πs,w\pi_{s,w} of a completion of the R-motivic sphere spectrum. We apply the ρ\rho-Bockstein spectral sequence to obtain R-motivic Ext groups from the C-motivic Ext groups, which are well-understood in a large range. These Ext groups are the input to the R-motivic Adams spectral sequence. We fully analyze the Adams differentials in a range, and we also analyze hidden extensions by ρ\rho, 2, and η\eta. As a consequence of our computations, we recover Mahowald invariants of many low-dimensional classical stable homotopy elements.

Keywords

Cite

@article{arxiv.2001.03606,
  title  = {R-motivic stable stems},
  author = {Eva Belmont and Daniel C. Isaksen},
  journal= {arXiv preprint arXiv:2001.03606},
  year   = {2020}
}
R2 v1 2026-06-23T13:08:19.107Z