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Cobordism categories, elliptic operators and positive scalar curvature

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HHHW04 - Manifolds

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)

This talk is part of the Isaac Newton Institute Seminar Series series.

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