On the curvature of 4-manifolds


Claude LeBrun

Stony Brook University

Harvard University

Thursday, May 20, 2004


Talk at 4:30 p.m. in Science Center D

Tea at 4:00 p.m. in the Math Lounge


Abstract:   A central problem in global differential geometry is to determine when a smooth compact n-manifold admits a metric which is "as flat as possible". In this lecture, I will describe some recent results on the existence and non-existence of such "optimal metrics" on simply connected 4-manifolds. Interestingly, the difference between existence and non-existence turns out to delicately depend on one's choice of differentiable structure; it is not determined by the homeomorphism type alone.


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Posted: May 11, 2004    URL: