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PRODID:-//Memento EPFL//
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SUMMARY:Characteristic classes as obstructions
DTSTART:20160927T101500
DTEND:20160927T113000
DTSTAMP:20260428T092659Z
UID:f328b3871d39ea97d3b1a469e42ba154bcba5d76a41a1d6a54e5526a
CATEGORIES:Conferences - Seminars
DESCRIPTION:Martina Rovelli (EPFL)\nCharacteristic classes are invariants 
 for principal bundles that take values in the cohomology of the base space
 . Every characteristic class captures different geometric features of prin
 cipal bundles. It is known\, for instance\, that the first Stiefel-Whitney
  class of an O(n)-bundle vanishes if and only if the bundle is orientable\
 , in which case the structure group can be reduced to SO(n). In the first 
 part of this talk\, we propose a uniform treatment to interpret most of th
 e studied characteristic classes as an obstruction to group reduction. By 
 plugging in the correct parameters\, the method recovers several classical
  theorems. Afterwards\, I will explain how the main result leads to the co
 nstruction of a long exact sequence of abelian groups for any principal bu
 ndle. This sequence involves the cohomology of the base space and the grou
 p cohomology of the structure group\, and the connecting map is deeply rel
 ated with the characteristic classes of the bundle.
LOCATION:CM 113
STATUS:CONFIRMED
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