OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
Proves that the L^(2)-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.
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MANUSCRIPT 01
The Singer conjecture in dimension four
We prove the four-dimensional Singer conjecture: the L^(2)-Betti numbers of the universal cover of a closed connected aspherical topological four-manifold vanish outside degree two. More generally, the same vanishing holds for finite connected aspherical integral Poincaré complexes of formal dimension four, including…
Full source abstract
We prove the four-dimensional Singer conjecture: the L^(2)-Betti numbers of the universal cover of a closed connected aspherical topological four-manifold vanish outside degree two. More generally, the same vanishing holds for finite connected aspherical integral Poincaré complexes of formal dimension four, including nonorientable ones.
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