A differential in the Adams spectral sequence for spheres
Abstract: In this talk we derive a $d_4$ differential in the mod $2$ Adams spectral sequence (to be abbreviated as ASS) for spheres. The ASS for spheres is a spectral sequence for computing $\pi_\ast^S$, the mod $2$ stable homotopy groups of spheres. The Kervaire invariant elements $\theta_n \in\pi_{2^{n+1}-2}^S$ for $n\ge1$ are stable homotopy elements detected by $h_n^2$ in the ASS for spheres. $\theta_n$ are known to be existent for $1\le n\le 5$, and recent development has shown that $\theta_n$ does not exist for $n\ge7$. The existence or non-existence of $\theta_6$ is yet to be known. In this talk we show that $d_4(h_6^3) =h_0^3g_4 \ne0$ in the ASS for spheres.
Tea Time: 3:30pm R707