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SUMMARY:Homotopy theory and the space of metrics of positive scalar  curva
 ture - Thomas Schick\, Goettingen
DTSTART:20160504T150000Z
DTEND:20160504T160000Z
UID:TALK62211@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:What is the topology of the space of metrics of positive scala
 r \ncurvature on a given manifold M? This question has received considerab
 le \nattention in recent years. An old construction of Hitchin shows how o
 ne \ncan use the action of the diffeomorphism group to construct interstin
 g \nelements in this space\, and use index theory to distinguish these. Th
 is \nallowed him to construct non-trivial components and classes in the \n
 fundamental group. A few years ago\, in joint work with Diarmuid Crowley\,
  \nwe showed that one can obtain non-trivial homotopy classes of \narbitra
 rily high degree. The main novelty lies in homotopy theory: we \nexploit t
 he non-trivial product structure of K-theory and stable \nhomotopy.\n\nIn 
 the talk\, we will describe this method and the work in progress which \na
 lso covers the remaining half of degrees. This is based on the use of \nTo
 da brackets\, a secondary product.\nAlong the way\, we get new information
  about the diffeomorphism group of \nspheres\, in particular about its Gro
 moll filtration
LOCATION:MR13
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