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

TL;DR

This paper constructs five new infinite families of simple η-torsion elements in stable homotopy groups of spheres, expanding understanding of their structure and relation to tmf-Hurewicz images.

Contribution

It introduces five 192-periodic families of simple η-torsion elements and analyzes their relation to tmf-Hurewicz images in stable stems.

Findings

Produced five 192-periodic infinite families of η-torsion elements.

Identified several other 192-periodic families in tmf-Hurewicz image as η-torsion.

Established trivial image under tmf-Hurewicz homomorphism for these families.

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.