The four-dimensional Singer conjecture
What the paper claims, in its own words
Proves that the L2-Betti numbers of the universal cover of every closed connected aspherical topological four-manifold vanish outside degree two. More generally, the same conclusion holds for every finite connected aspherical integral Poincaré complex of formal dimension four, proving the four-dimensional Singer conjecture in this wider class.
The plain-language explainer for this entry is still coming.
The original paper
- The Singer conjecture in dimension four (PDF, opens in a new tab) September 25, 2026