Year: 2026
Type: preprint
Abstract: We construct a smooth Riemannian metric with strictly positive sectional curvature on \(S^3\times S^3\). Since \(S^3\times S^3\) is even-dimensional and has Euler characteristic zero, our result disproves the positive-curvature case of Hopf's sign conjecture. The metric and the proof were discovered by the Odin Automatic AI Research Agent.
Source: arXiv (Cornell University)
Authors: Guo, Shengtao, Fang, Ethan X., Lu, Junwei
Institution: Harvard University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212693265