arXiv subjects

Akira Tominaga

Publications and source records attributed to Akira Tominaga.

2 recordsLinked to original sources

arXiv2026

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.

math.AT↗

arXiv2025

Genuine $C_n$-equivariant $\mathrm{TMF}$

We determine the $\mathrm{TMF}$-module structures of the genuine $C_2$-equivariant $\mathrm{TMF}$ with $\mathrm{RO}(C_2)$-gradings and of the $C_3$-equivariant $\mathrm{TMF}$. Moreover, we propose a general strategy for studying $C_n$-equivariant $\mathrm{TMF}$ via $U(1)$-equivariant $\mathrm{TMF}$ and a duality phenomenon in equivariant $\mathrm{TMF}$.

math.AT↗