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Homotopy 7-spheres and positive scalar curvature

Song Jin RI
Schedule: 
Friday, May 22, 2020 - 11:00
Location: 
Online
Location: 
Zoom (sign in to get the link)
Abstract: 

The main goal of the webinar is to show that every homotopy 7-sphere, which is homeomorphic (but possibly not diffeomorphic) to the standard 7-sphere, admits a Riemannian metric with positive scalar curvature. I will first show that under the connected sum operation, homotopy 7-spheres form an abelian group, which is isomorphic to the cyclic group of order 28. Then I will move on to show that the Gromoll-Meyer 7-sphere, as a generator of the group, admits a Riemannian metric of positive scalar curvature. The main goal follows from a theorem of Gromov-Lawson and Schoen-Yau. The talk is based on [Kervaire and Milnor, 1963] and [Gromoll-Meyer, 1974].

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