Geometry and Topology Seminar

Series: Geometry and Topology Seminar Series

On the topology of the manifolds with positive intermediate curvature

Xuan Yao, Department of Mathematics, Cornell University,

We formulate a conjecture relating the topology of a manifold's universal cover with the existence of metrics with positive m-intermediate curvature. We prove the result for manifolds of dimension n∈{3,4,5} and for most choices of m when n=6. As a corollary, we show that a closed, aspherical 6-manifold cannot admit a metric with positive 4-intermediate curvature.

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