On the tmf-Hurewicz image of $A_1$

TL;DR

This paper proves that the $tmf$-Hurewicz map for a class of finite spectra with specific mod-2 cohomology is surjective, advancing understanding of the relationship between $A_1$ spectra and topological modular forms.

Contribution

It establishes the surjectivity of the $tmf$-Hurewicz image for spectra with mod-2 cohomology isomorphic to $ ext{A}(1)$, a new result in the field.

Findings

$tmf$-Hurewicz image of $A_1$ is surjective.

Provides new insights into the structure of $A_1$ spectra.

Enhances understanding of the connection between $A_1$ and topological modular forms.

Abstract

Let $A_1$ be any spectrum in the class of finite spectra whose mod-2 cohomology is isomorphic to $\mathcal{A}(1)$ as a module over the subalgebra $\mathcal{A}(1)$ of the Steenrod algebra; let $tmf$ be the connective spectrum of topological modular forms. In this paper, we prove that the $tmf$-Hurewicz image of $A_1$ is surjective.