$C_3$-equivariant stable stems

Yueshi Hou; Shangjie Zhang

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arXiv · 2505.10745

$C_3$-equivariant stable stems

Yueshi Hou·Shangjie Zhang

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Abstract

We compute the spoke-graded $C_3$-equivariant stable homotopy groups of spheres $π_{i, j}^{C_3}$, 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 $j=2k$, this corresponds to the usual $RO(C_3)$-graded homotopy groups of spheres $π^{C_3}_{i-j+kλ}$ for some fixed 2-dimensional $C_3$-faithful representation $λ$. We also describe the geometric fixed point map $Φ^{C_3}: π_{i, j}^{C_3}\to π_{i-j}^{cl}$ and the underlying map $Res: π_{i, j}^{C_3}\to π_{i}^{cl}$.

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BibTeX RIS

Yueshi Hou, Shangjie Zhang. 2026-04-19. $C_3$-equivariant stable stems. https://arxiv.org/abs/2505.10745

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