For finite abelian G with Sylow p-subgroup N_p, the KU_G/p-local sphere equals homotopy fixed points of a p-complete KO_{N_p}-module and a wedge of equivariant Morava K-theory spheres, with computed Z-graded and RO(G)-graded homotopy Mackey functors.
$C_3$-equivariant stable stems
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abstract
We compute the spoke-graded $C_3$-equivariant stable homotopy groups of spheres $\pi_{i, j}^{C_3}$, 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 $\pi^{C_3}_{i-j+k\lambda}$ for some fixed 2-dimensional $C_3$-faithful representation $\lambda$. We also describe the geometric fixed point map $\Phi^{C_3}: \pi_{i, j}^{C_3}\to \pi_{i-j}^{cl}$ and the underlying map $Res: \pi_{i, j}^{C_3}\to \pi_{i}^{cl}$.
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math.AT 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Extends Burklund-Lin-Wang-Xu techniques to cofiber-of-τ formalism for hidden extensions and derives new exotic transfer differentials in C4-slice spectral sequences for BP((C4))<m>.
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On the equivariant $KU_G$-local sphere for finite abelian groups
For finite abelian G with Sylow p-subgroup N_p, the KU_G/p-local sphere equals homotopy fixed points of a p-complete KO_{N_p}-module and a wedge of equivariant Morava K-theory spheres, with computed Z-graded and RO(G)-graded homotopy Mackey functors.
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Burklund-Lin-Wang-Xu Methods in the Cofiber-of-Tau Formalism and Applications to Equivariant Slice Differentials
Extends Burklund-Lin-Wang-Xu techniques to cofiber-of-τ formalism for hidden extensions and derives new exotic transfer differentials in C4-slice spectral sequences for BP((C4))<m>.