3 problems

Let $M(\alpha)$ denote the Mahowald invariant of a 2-primary stable homotopy class $\alpha$, and let $\nu_n$-periodic and $\nu_{n+1}$-periodic families be periodic families in the…

Chromatic redshift conjecture. If $\alpha \notin M_{\mathbb{K}}(\alpha)$, then $M_{\mathbb{K}}(\alpha)$ consists entirely of $v_n$-torsion elements. If $w:\Sigma^dY\to Y$ is a powe…

Let $S$ denote the sphere spectrum, and let $R_S$ be the $S$-based Mahowald invariant, a partially defined and multivalued relation on $\pi_*S$. Let $\theta_j$ denote the Kervaire…