A three-manifold without conjugate points or nonpositive curvature
What the paper claims, in its own words
Constructs a closed connected orientable smooth three-manifold that admits a metric without conjugate points but no metric of nonpositive sectional curvature. This answers negatively, already in dimension three, whether the first metric-existence property implies the second.
The plain-language explainer for this entry is still coming.
The original paper
- A Three-Manifold Without Conjugate Points and Without a Nonpositively Curved Metric (PDF, opens in a new tab) September 24, 2026 Formal proof listed