Positive scalar curvature forces rational inessentiality
We prove that every closed connected oriented smooth manifold admitting strictly positive scalar curvature is rationally inessential: its rational fundamental class maps to zero under the classifying map. No spin or fundamental-group hypothesis is needed, and there is no upper dimension bound. This proves the Gromov–Lawson aspherical conjecture; moreover, every nonnegative-scalar-curvature metric on a closed aspherical manifold is flat. We also show that every closed oriented smooth manifold of positive dimension with nonnegative scalar curvature has zero real simplicial volume, proving the…
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100+ reactions to 100+ solutionsProofs and PromptsOct 8, 2026
This trick and these two papers now appear in OpenAI’s deeply creative solutions of problems 207 and 335 – problems so different, they could not be farther apart! I am stunned. What do I take away from this night? We cannot defensively narrow our focus to what we currently regard as human…