$C_3$-equivariant stable stems

Yueshi Hou; Shangjie Zhang

paper

$C_{3}$ -equivariant stable stems

arXiv:2505.10745

Abstract

We compute the spoke-graded $C_{3}$ -equivariant stable homotopy groups of spheres $I ¨ _{i, j}^{C_{3}}$ , for stems less than 25 (i.e. $i \leq 25$ ) and for weights between -16 and 16 (i.e. $- 16 \leq j \leq 16$ ). In particular, for $j = 2 k$ , this corresponds to the usual $R O (C_{3})$ -graded homotopy groups of spheres $I ¨ _{i - j + k I^»}^{C_{3}}$ for some fixed 2-dimensional $C_{3}$ -faithful representation $I^»$ . We also describe the geometric fixed point map $I^¦^{C_{3}} : I ¨ _{i, j}^{C_{3}} \to I ¨ _{i - j}^{c l}$ and the underlying map $R es : I ¨ _{i, j}^{C_{3}} \to I ¨ _{i}^{c l}$ .

Updated introduction and minor revisions. Comments are welcomed

C3​-equivariant stable stems

Abstract

$C_{3}$ -equivariant stable stems