2024/07/04 by Thomas Bruun Madsen, Andrew Swann, Madsen, Thomas Bruun +1
Computer Science · Mathematics · #53C25 (Primary) 32Q25 #53C26 #53C29 #53C55 #53D20 (Secondary) #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2407.03693
openalex publication_date 2024/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study complete, simply-connected manifolds with special holonomy that are toric with respect to their multi-moment maps. We consider the cases where there is a connected non-Abelian symmetry group containing the torus. For Spin(7)-manifolds, we show that the only possibility are structures with a cohomogeneity-two action of T3 × SU(2). We then specialise the analysis to holonomy G2, to Calabi-Yau geometries in real dimension six and to hyperKähler four-manifolds. Finally, we consider weakly coherent triples on ℝ × SU(2), and their extensions over singular orbits, to give local examples in the Spin(7)-case that have singular orbits where the stabiliser is of rank one.