Topological Jacobi Forms

Abstract

As a generalization of the ring spectrum of topological modular forms, we construct a graded ring spectrum of topological Jacobi forms, ${\mathrm{TJF}}_{\ast }$. This is constructed as the global sections of a sheaf of $E_{\infty }$-ring spectra on the stacky universal elliptic curve using circle-equivariant $\mathrm{TMF}$. Complete calculations of its homotopy at odd primes and partial results at $p=2$ are given.

41 pages, several charts in color