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.

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

References in corpus (2)

• (Topological) modular forms with level structures: decompositions and duality
• Elliptic genera of level $N$ for complete intersections

Cited by in corpus (1)

• Elliptic cohomology is unique up to homotopy