On Bott-Chern and Aeppli cohomologies of two-dimensional toroidal groups

2025/09/08 by Jinichiro Tanaka, Tanaka, Jinichiro
Mathematics · #32L10 #53C55 #Advanced Operator Algebra Research #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2509.06384

openalex publication_date 2025/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

A toroidal group is a generalization of a complex torus, and is obtained as the quotient of the complex Euclidean space ℂⁿ by a discrete subgroup. Toroidal groups with finite-dimensional cohomology, called theta toroidal groups, are known to exhibit behavior analogous to that of complex tori. We compute Bott--Chern and Aeppli cohomologies for two-dimensional non-compact theta toroidal groups.

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