Title: Manifolds and the Kervaire invariant
Speaker: Paul VanKoughnett
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Abstract:
Last week, I defined a close relationship between objects of stable homotopy theory -- the homotopy groups of spheres -- and objects of geometry -- framed manifolds. This relationship will allow us to construct and discuss Kervaire's 1960 example of a 10-manifold admitting no differentiable structure. This example is the starting point of the Kervaire invariant problem, which was almost completely resolved recently using some high-powered methods of homotopy theory.Date: Friday, October 31, 2014