Geometry Forum (special edition)
Tuesday, April 7, 2009, 8:30am, 227 Physics
Jeff Jauregui (Duke University)
Four-manifolds without Einstein metrics
Abstract:
This talk focuses on two papers by C. Lebrun from the 1990s in which he finds a large class of 4-manifolds which do not carry Einstein metrics. I'll begin by explaining the famous Hitchin--Thorpe inequality. Gauge theory will enter the picture through the Seiberg--Witten equations and the associated Weitzenbock formula. Other tools we'll use are the generalized Gauss--Bonnet Theorem, Hirzebruch Signature Theorem, and a little algebraic geometry. If time permits, I'll mention some applications to computing Yamabe invariants of complex surfaces.

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