Positive scalar curvature and non commutative geometry
by
Guihua Gong
University of Puerto Rico

Gromov conjectured that "A uniformly contractible complete Riemannian manifold can not have uniformly positive scalar curvature." Scalar curvature is a local invariant of a smooth manifold. This conjecture gives the information about global behavior (contractibility) of the manifold from the local invariant (scalar curvature) of the manifold. In a joint work with G. Yu, we proved that the Gromov conjecture holds for manifolds with subexponential volume growth. In this talk, we will present this result with explanation of why non commutative geometry is involved.

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Date received: January 25, 2008