Connective Models for Topological Modular Forms of Level $n$

TL;DR

This paper constructs connective versions of topological modular forms of higher level, enabling the realization of Hirzebruch's level-$n$ genus as a ring spectrum map, advancing the understanding of modular forms in stable homotopy theory.

Contribution

It introduces connective models for topological modular forms of level $n$, providing a new framework to realize classical genera as maps of ring spectra.

Findings

Constructed connective models for $ ext{tmf}_1(n)$

Realized Hirzebruch's level-$n$ genus as a ring spectrum map

Enhanced the understanding of modular forms in stable homotopy theory

Abstract

The goal of this article is to construct and study connective versions of topological modular forms of higher level like $\mathrm{tmf}_1(n)$. In particular, we use them to realize Hirzebruch's level-$n$ genus as a map of ring spectra.