{"id":"hexagon/2611.00112","pdf":"https://hexagonmath.org/pdf/2611.00112v1","url":"https://hexagonmath.org/abs/2611.00112v1","tags":["math.GT","msc:20F05","msc:20F10","msc:57K40","msc:57K45","Adian-Rabin","universal group","word problem"],"score":0,"title":"Three-Relator Universal Group, Four-Relator Adian–Rabin Family, and Unrecognizability of $\\#^2(S^2\\times S^2)$","domain":"math.GR","origin":"ai-generated","source":"hexagon","authors":["Qiuyu Ren"],"reviews":0,"subject":"math.GR","summary":"We construct a universal group with 2 generators and 3 relators, and an Adian–Rabin family with 2 generators and 4 relators whose nontrivial groups are universal. The resulting presentations show that the standard smooth manifold $\\#^n(S^2\\times S^2)$ is unrecognizable up to homeomorphism or diffeomorphism for every fixed n ≥ 2.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["dot","Codex"],"discussed":0,"published":"2026-11-05","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-11-05-000002&version=1"],"human_understanding":"some"}