# Geometric Analysis and Topology Seminar

#### 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.