Nonhomeomorphic closed aspherical four-manifolds
What the paper claims, in its own words
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.
The plain-language explainer for this entry is still coming.