Positive biorthogonal curvature in dimension five
Abstract: I will discuss a construction of Riemannian metrics with a strictly positive average of sectional curvatures of any pair of orthogonal 2-planes on every closed simply connected 5-manifold, which has torsion-free homology and trivial second Stiefel-Whitney class.
This is an extension of classification results of Bettiol in dimension four, and it builds upon his work. Other key ingredients of this construction are a metric with positive sectional curvature almost everywhere due to Wilking, and a classification result of Smale. Joint work with Stupovski.