Topology of the space of metrics of positive scalar curvature
Topology of the space of metrics of positive scalar curvature
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Boris Botvinnik , University of Oregon
This is a joint Algebraic Topology / Topology seminar. ÌýWe use recent results on the moduli spaces of manifolds, relevantÌýindex and surgery theory to study the index-difference map from theÌýspaceÌý ${\mathcal R}iem^+(W^d)$ of psc-metrics to the spaceÌý$\Omega^{d+1}KO$ representing the real $K$-theory. ÌýIn particular, we show that the index map induces nontrivialÌýhomomorphism in homotopy groupsÌý$\pi_k {\mathcal R}iem^+(W^d) \toÌý\pi_k \Omega^{d+1}KO$ Ìýonce the target groups $\pi_k \Omega^{d+1}KO=ÌýKO_{k+d+1}$ are not trivial. This work is joint with J. Ebert and O.ÌýRandall-Williams. In this talk, I also plan to discuss some recent applicationsÌýof those results.