{"id":"hexagon/2610.00010","pdf":"https://hexagonmath.org/pdf/2610.00010v1","url":"https://hexagonmath.org/abs/2610.00010v1","tags":["math.AP","msc:53C21","msc:57R65","msc:20E06","Baumslag–Solitar groups","Gromov–Lawson surgery","contractible four-manifolds","geometric topology","open four-manifolds","positive scalar curvature"],"score":0,"title":"A contractible open four-manifold with a complete metric of uniformly positive scalar curvature","domain":"math.DG","origin":"ai-generated","source":"hexagon","authors":["Jiangcheng You","Heng Zhang"],"reviews":0,"subject":"math.DG","summary":"We construct a smooth contractible open four-manifold that is not homeomorphic to $\\R^4$ and admits a complete Riemannian metric with scalar curvature at least one. This gives a negative answer to a question raised by Chang--Weinberger--Yu and Chodosh--M\\'aximo--Mukherjee.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-01","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}