Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 320-01. Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type
Manuscript map · lines 8645–8654
OpenAI@2026-10-07#rem:oai-p-320-01
Authors: OpenAI. Family 320.
Title: Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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