Cohomological lifting of multi-toric graphs

2024/12/20 by Kael Dixon, Dixon, Kael, Thomas Bruun Madsen +3
Computer Science · Mathematics · #53C25 (Primary) 14M25 #53C26 #53C29 #53D20 (Secondary) #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2412.15769

openalex publication_date 2024/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study G₂-manifolds obtained from circle bundles over symplectic SU(3)-manifolds with T²-symmetry. When the geometry is multi-Hamiltonian, we show how the compact part of the resulting multi-moment graph for the G₂-structure may obtained cohomologically from the base. The lifting procedure is illustrated in the context of toric geometry.

Related

• Multi-toric geometries with larger compact symmetry
• Nearly Parallel G₂-Structures with Torus Symmetry
• Four dimensions from two in symplectic topology
• A construction of G₂-manifolds from K3 surfaces with a ℤ²₂-action
• Circle actions on symplectic four-manifolds