Cohomology of Jacobi forms
Number Theory
2025-10-20 v6 Functional Analysis
Abstract
We define and compute a cohomology of the space of Jacobi forms based on precise analogues of Zhu reduction formulas. A counterpart of the Bott-Segal theorem for the reduction cohomology of Jacobi forms on the torus is proven. It is shown that the reduction cohomology for Jacobi forms is given by the cohomology of -point connections over a deformed vertex operator algebra bundle defined on the torus. The reduction cohomology for Jacobi forms for a vertex operator algebra is determined in terms of the space of analytical continuations of solutions to Knizhnik-Zamolodchikov equations.
Cite
@article{arxiv.2106.07773,
title = {Cohomology of Jacobi forms},
author = {A. Zuevsky},
journal= {arXiv preprint arXiv:2106.07773},
year = {2025}
}