Connective Models for Topological Modular Forms of Level $n$

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.Comment: 27 pages; v2: added several clarifications and minor correcionts in response to referee's comments, final version to appear in AG