{"id":"openai-math/A-PD4-group-without-an-aspherical-manifold-model","pdf":"https://github.com/openai/math/blob/main/preprints/A-PD4-group-without-an-aspherical-manifold-model-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-PD4-group-without-an-aspherical-manifold-model-September-24-2026","tags":["geometric-group-theory","poincare-duality","topology"],"score":0,"title":"A PD4 group without an aspherical manifold model","domain":"Topology","family":"305","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"We construct a finitely presented integral Poincaré duality group of dimension four that has a finite classifying space but is not the fundamental group of any closed aspherical topological four-manifold. This gives a negative answer to Wall's manifold-realization question in dimension four.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Four-dimensional disk embedding and Wall's conjecture"}