{"paper":{"title":"Special metrics and Triality","arxiv_id":"math/0602414","primary_cat":"math.DG","submitted_at":"2006-02-19T19:14:09+00:00","version_compiled":"v3"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. 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$\\Delta\\otimes\\Lambda^1$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.14,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.2,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.79,"interpretation":0.0}},{"i":2,"p":0.73,"id":"s2","own":true,"role":"result","text":"We establish various obstructions to the existence of topological reductions to PSU(3).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.73,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.27,"interpretation":0.0}},{"i":3,"p":0.61,"id":"s3","own":true,"role":"result","text":"For compact manifolds, we also give sufficient conditions for topological PSU(3)-structures that can be lifted to topological SU(3)-structures.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.61,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.39,"interpretation":0.0}},{"i":4,"p":0.64,"id":"s4","own":true,"role":"result","text":"We also construct the first known compact example of an integrable non-symmetric PSU(3)-structure.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.23,"quantitative":false,"quantitative_p":0.45,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.64,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.36,"interpretation":0.0}},{"i":5,"p":0.95,"id":"s5","own":true,"role":"contribution","text":"In the same vein, we give a new Riemannian characterisation for topological quaternionic K\\\"ahler structures which are defined by an $Sp(1)\\cdot Sp(2)$-invariant self-dual 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