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SUMMARY:Relative kappa-classes - Diarmuid Crowley (University of Melbourne
 )
DTSTART:20181207T143000Z
DTEND:20181207T153000Z
UID:TALK115480@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Diff(D^n)\, the the space of diffeomorphisms of the n-disc fix
 ed near the boundary has rich rational topology.  For example\, Weiss&#39\
 ;s discovery of ``surreal&#39\;&#39\; Pontrjagin classes leads to the exis
 tence of rationally non-trivial homotopy classes in BDiff(D^n).  <br> <br>
  For any smooth n-manifold M\, extension by the identity induces a map BDi
 ff(D^n) \\to BDiff(M).  In this talk I will report on joint work with Wolf
 gang Steimle and Thomas Schick\, where we consider the problem of computin
 g the image of the ``Weiss classes&#39\;&#39\; under the maps on homotopy 
 and homology induced by extension.  This problem naturally leads one to co
 nsider relative kappa-classes.<br> <br> Via relative kappa-classes\, we sh
 ow that the maps induced by extension are rationally non-trivial for a wid
 e class of manifolds M\, including aspherical manifolds (homology\, hence 
 also homotopy) and stably parallelisable manifolds (homotopy).  When M is 
 aspherical\, our arguments rely on vanishing results for kappa-classes due
  to Hebestreit\, Land\, Lueck and Randal-Williams.<br> <br>
LOCATION:Seminar Room 1\, Newton Institute
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