New simple $\eta$-torsion families of elements in the stable stems

Abstract

We produce five 192-periodic infinite families of simple $\eta$-torsion elements in the stable homotopy groups of spheres with trivial image under the tmf-Hurewicz homomorphism. We also establish that several other 192-periodic families in the stable stems, which are in the tmf-Hurewicz image, consist of simple $\eta$-torsion elements.