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Cobordism categories, elliptic operators and positive scalar curvature

Presented by: 
Johannes Ebert
Thursday 6th December 2018 - 10:00 to 11:00
INI Seminar Room 1
We prove that a certain collection of path components of the space of metrics of positive scalar curvature on a high-dimensional sphere has the homotopy type of an infinite loop space, generalizing a theorem by Walsh. The proof uses an version of the surgery method by Galatius and Randal--Williams to cobordism categories of manifolds equipped with metrics of positive scalar curvature. Moreover, we prove that the secondary index invariant of the spin Dirac operator is an infinite loop map. The proof of that fact uses a generalization of the Atiyah--Singer index theorem to spaces of manifolds. (Joint work with Randal--Williams)
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons