English

Towards the $p=3$ Kervaire Invariant Problem: The $E_2$-page for the homotopy fixed points spectral sequence computing $\pi_*({E_6}^{hC_9})$

Algebraic Topology 2025-07-15 v1

Abstract

Hill, Hopkins, and Ravenel suggest that the last remaining Kervaire invariant problem, the case of p=3p=3, can be solved by computing the homotopy fixed points spectral sequence for πE6hC9\pi_* E_6^{hC_9}. We prove a detection theorem for this case and use a conjectural form of the C9C_9-action on E6E_6 to compute the E2E_2 page of this spectral sequence away from homological degree zero.

Keywords

Cite

@article{arxiv.2507.10157,
  title  = {Towards the $p=3$ Kervaire Invariant Problem: The $E_2$-page for the homotopy fixed points spectral sequence computing $\pi_*({E_6}^{hC_9})$},
  author = {Eva Belmont and Rin Ray},
  journal= {arXiv preprint arXiv:2507.10157},
  year   = {2025}
}