University of Cambridge > Talks.cam > Differential Geometry and Topology Seminar > Infinite loop spaces and positive scalar curvature in the presence of a fundamental group

Infinite loop spaces and positive scalar curvature in the presence of a fundamental group

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  • UserJohannes Ebert, Muenster
  • ClockWednesday 27 April 2016, 16:00-17:00
  • HouseMR13.

If you have a question about this talk, please contact Ivan Smith.

For each spin manifold M of dimension d, there is a map `inddiff’ from the space Riem+(M) of metrics of positive scalar curvature metrics on M to the classifying space for the real K-theory functor KO{-d-1}. This map is constructed as a secondary index invariant. In joint work with Botvinnik and Randal-Williams, we constructed maps from a certain infinite loop space into Riem+(M) (for d at least 6) which allowed us to show, among other things that `inddiff’ is surjective in rational homotopy.

In this talk, I will talk about a continuation of this project, which takes the fundamental group of a manifold into account. In that case, `inddiff’ takes values in the K-theory of the reduced group C*-algebra of the fundamental group of M, and under fairly general assumptions on that group, we can prove rational surjectivity for this refined index invariant.

This talk is part of the Differential Geometry and Topology Seminar series.

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