Topological Jacobi Forms

2025/08/11 by Tilman Bauer, Bauer, Tilman, Lennart Meier +1 · 1 citation
Mathematics · #11F50 #55N20 #55N34 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2508.08010

openalex publication_date 2025/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• A new approach to (3+1)-dimensional TQFTs via topological modular forms
• Topological Elliptic Genera I -- The mathematical foundation
• Global 2-rings and genuine refinements
• Global homotopy theory via partially lax limits
• The localized slice spectral sequence, norms of Real bordism, and the Segal conjecture
• On equivariant topological modular forms
• Graded rings of integral Jacobi forms
• Meromorphic Jacobi Forms of Half-Integral Index and Umbral Moonshine Modules
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
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• Morita theory for Hopf algebroids and presheaves of groupoids

Cited by

• Spectral moduli problems for level structures and an integral Jacquet-Langlands dual of Morava E-theory

Related

• Graded rings of integral Jacobi forms
• On equivariant topological modular forms
• Topological modular forms with level structure
• Strictly commutative realizations of diagrams over the Steenrod algebra\n and topological modular forms at the prime 2
• Whitehead Filtrations for Computations in Topological Hochschild Homology