Computations of topological Jacobi forms

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.

💡 Research Summary

This paper presents a complete 2‑local computation of the homotopy groups of the spectra of topological Jacobi forms (TJF) for every index $m\ge1$. The authors work within the framework of equivariant topological modular forms (TMF) and exploit a TMF‑cellular decomposition to reduce the problem to a finite CW‑complex $P_m$ that has exactly one even cell in each dimension $2d\le2m$ (except $d=1$). The main results are twofold. First, they prove an equivalence of TMF‑modules \