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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Infinite loop spaces and positive scalar curvature
in the presence of a fundamental group - Johannes
Ebert\, Muenster
DTSTART;TZID=Europe/London:20160427T160000
DTEND;TZID=Europe/London:20160427T170000
UID:TALK63226AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/63226
DESCRIPTION:For each spin manifold M of dimension d\, there is
a map `inddiff' from the space Riem+(M) of metric
s of positive scalar curvature metrics on M to the
classifying space for the real K-theory functor K
O{-d-1}. This map is constructed as a secondary in
dex invariant. In joint work with Botvinnik and Ra
ndal-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.
\n\nIn this talk\, I will talk about a continuatio
n of this project\, which takes the fundamental gr
oup of a manifold into account. In that case\, `in
ddiff' 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 ref
ined index invariant.
LOCATION:MR13
CONTACT:Ivan Smith
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