Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type
We construct closed connected aspherical topological four-manifolds that are homotopy equivalent but not homeomorphic, disproving the homeomorphism-existence formulation of the Borel conjecture in dimension four. Their common fundamental group is word-hyperbolic. One of the manifolds also has a self-homotopy equivalence not homotopic to a homeomorphism.
Cite
@misc{OAI:Nonhomeomorphic-closed-aspherical-four-manifolds-with-the-same-homotopy-type-October-4-2026,
author = {{OpenAI}},
title = {{Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Nonhomeomorphic-closed-aspherical-four-manifolds-with-the-same-homotopy-type-October-4-2026/paper.pdf}{OAI:Nonhomeomorphic-closed-aspherical-four-manifolds-with-the-same-homotopy-type-October-4-2026}},
year = {2026}
}