{"paper":{"title":"Multi-toric geometries with larger compact symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrew Swann, Thomas Bruun Madsen","submitted_at":"2024-07-04T07:27:53Z","abstract_excerpt":"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 $\\mathrm{Spin}(7)$-manifolds, we show that the only possibility are structures with a cohomogeneity-two action of $T^{3} \\times \\mathrm{SU}(2)$. We then specialise the analysis to holonomy $G_{2}$, to Calabi-Yau geometries in real dimension six and to hyperK\\\"ahler four-manifolds. Finally, we consider weakly coherent triples on $\\mathbb{R} \\times \\mathrm{SU}(2)$, and thei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.03693","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.03693/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}