English

$C_3$-equivariant stable stems

Algebraic Topology 2026-04-21 v2

Abstract

We compute the spoke-graded C3C_3-equivariant stable homotopy groups of spheres πi,jC3\pi_{i, j}^{C_3}, for stems less than 25 (i.e. i25i\leq 25) and for weights between -16 and 16 (i.e. 16j16-16\leq j\leq 16). In particular, for j=2kj=2k, this corresponds to the usual RO(C3)RO(C_3)-graded homotopy groups of spheres πij+kλC3\pi^{C_3}_{i-j+k\lambda} for some fixed 2-dimensional C3C_3-faithful representation λ\lambda. We also describe the geometric fixed point map ΦC3:πi,jC3πijcl\Phi^{C_3}: \pi_{i, j}^{C_3}\to \pi_{i-j}^{cl} and the underlying map Res:πi,jC3πiclRes: \pi_{i, j}^{C_3}\to \pi_{i}^{cl}.

Keywords

Cite

@article{arxiv.2505.10745,
  title  = {$C_3$-equivariant stable stems},
  author = {Yueshi Hou and Shangjie Zhang},
  journal= {arXiv preprint arXiv:2505.10745},
  year   = {2026}
}

Comments

Updated introduction and minor revisions. Comments are welcomed

R2 v1 2026-06-28T23:35:10.157Z