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SUMMARY:Infinite loop spaces and positive scalar curvature in the presence
  of a fundamental group - Johannes Ebert\, Muenster
DTSTART:20160427T150000Z
DTEND:20160427T160000Z
UID:TALK63226@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:For each spin manifold M of dimension d\, there is a map `indd
 iff' from the space Riem+(M) of metrics of positive scalar curvature metri
 cs on M to the classifying space for the real K-theory functor KO{-d-1}. T
 his map is constructed as a secondary index invariant. In joint work with 
 Botvinnik and Randal-Williams\, we constructed maps from a certain infinit
 e loop space into Riem+(M) (for d at least 6) which allowed us to show\, a
 mong other things that `inddiff' is surjective in rational homotopy.\n\nIn
  this talk\, I will talk about a continuation of this project\, which take
 s the fundamental group of a manifold into account. In that case\, `inddif
 f' takes values in the K-theory of the reduced group C*-algebra of the fun
 damental group of M\, and under fairly general assumptions on that group\,
  we can prove rational surjectivity for this refined index invariant.
LOCATION:MR13
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