New infinite families in the stable homotopy groups of spheres

Abstract

We identify seven new $192$-periodic infinite families of elements in the $2$-primary stable homotopy groups of spheres. Although their Hurewicz image is trivial for topological modular forms, they remain nontrivial after $\mathrm{T}(2)$- as well as $\mathrm{K}(2)$-localization. We also obtain new information about $2$-torsion and $2$-divisibility of some of the previously known $192$-periodic infinite families in the stable stems.