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Topology/Geometry Seminar

The Inequalities of Hitchin-Thorpe and Thorpe

Brian Klatt (Rutgers)

Location:  Hill 525
Date & time: Tuesday, 11 September 2018 at 3:40PM - 4:40PM

ABSTRACT:  J. A. Thorpe and N. Hitchin independently discovered that the Euler characteristic and signature of a compact, oriented, 4-dimensional Einstein manifold must satisfy a remarkable inequality. As a consequence there are infinitely many simply-connected topological manifolds that cannot support an Einstein metric. An underemphasized aspect of the story of this so-called Hitchin-Thorpe inequality is that it is only a special case of Thorpe's original and more general inequality.

In this talk, we give some background on the classical Hitchin-Thorpe inequality as well as Thorpe's inequality before discussing our recent Generalized Thorpe Inequality, which identifies the classical inequalities as resulting from a pure result in Chern-Weil theory.

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