Constructs closed connected aspherical topological four-manifolds that are homotopy equivalent but not homeomorphic, with a common word-hyperbolic fundamental group. This disproves even the homeomorphism-existence formulation of the Borel conjecture in dimension four.
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In Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type, 4 October 2026
Possible match to OpenAI’s description, selected from the papers’ main statements because it shares the most wording. No review confirming the selection is recorded.
There exist closed connected aspherical topological four-manifolds M and N that are homotopy equivalent but not homeomorphic. Their common fundamental group is word-hyperbolic.
In Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type, 4 October 2026
Possible match to OpenAI’s description, selected from shared wording. No review confirming the selection is recorded.
There exist a closed connected aspherical topological four-manifold M and a homotopy equivalence f\colon M\to M such that no homeomorphism M\to M is homotopic to f.
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Why this passage is shown
Theorem 1.1
In Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type, 4 October 2026
Why this passage is shown
Theorem 1.2
In Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type, 4 October 2026