Geometric Analysis and Topology Seminar

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Topology of the Space of Metrics of Positive Scalar Curvature

Speaker: Boris Botvinnik, University of Oregon

Location: Warren Weaver Hall 512

Date: Monday, December 4, 2017, 11 a.m.

Synopsis:

We use recent results on the moduli spaces of manifolds, relevant index and surgery theory to study the index-difference map from the space \(\mathcal{R}^+(W^d)\) of psc-metrics to the space \(\Omega^{d+1}KO\) representing the real \(K\)-theory. In particular, we show that the index-difference map induces nontrivial homomorphism in homotopy groups \(\pi_k \mathcal{R}^+(W^d) \rightarrow \pi_k \Omega^{d+1}KO\) once the target groups \(\pi_k \Omega^{d+1}KO = KO_{k+d+1}\) are not trivial. This work is joint with J. Ebert and O. Randall-Williams. In this talk, I also plan to discuss related recent results on the space of positive Ricci curvature.