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Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type

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OpenAI Mathopenai-math/Nonhomeomorphic-closed-aspherical-four-manifolds-with-the-same-homotopy-typeOct 4, 2026math.GTAI-generatedscore 0

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.

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