Computations of topological Jacobi forms

Abstract

We compute, at the prime $2$, the entire descent spectral sequence converging to the homotopy groups of the spectra of topological Jacobi forms $\mathrm{TJF}_m$ for every index $m \geq 1$. An explicit $\mathrm{TMF}$-cellular decomposition $\mathrm{TJF}_m \simeq \mathrm{TMF} \otimes P_m$ reduces the problem to analyzing a finite complex $P_m$ with one even cell in each dimension $\leq 2m$ except $2$. We identify all differentials using the cell structure.