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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Homotopy theory and the space of metrics of positi
ve scalar curvature - Thomas Schick\, Goettingen
DTSTART;TZID=Europe/London:20160504T160000
DTEND;TZID=Europe/London:20160504T170000
UID:TALK62211AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/62211
DESCRIPTION:What is the topology of the space of metrics of po
sitive scalar \ncurvature on a given manifold M? T
his question has received considerable \nattention
in recent years. An old construction of Hitchin s
hows how one \ncan use the action of the diffeomor
phism group to construct intersting \nelements in
this space\, and use index theory to distinguish t
hese. This \nallowed him to construct non-trivial
components and classes in the \nfundamental group.
A few years ago\, in joint work with Diarmuid Cro
wley\, \nwe showed that one can obtain non-trivial
homotopy classes of \narbitrarily high degree. Th
e main novelty lies in homotopy theory: we \nexplo
it the non-trivial product structure of K-theory a
nd stable \nhomotopy.\n\nIn the talk\, we will des
cribe this method and the work in progress which \
nalso covers the remaining half of degrees. This i
s based on the use of \nToda brackets\, a secondar
y product.\nAlong the way\, we get new information
about the diffeomorphism group of \nspheres\, in
particular about its Gromoll filtration
LOCATION:MR13
CONTACT:Ivan Smith
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