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SUMMARY:Topological Invariants for G-kernels and Group Actions - Ulrich Pe
 nnig (Cardiff University)
DTSTART:20241205T115000Z
DTEND:20241205T123000Z
UID:TALK218644@talks.cam.ac.uk
DESCRIPTION:A G-kernel is a group homomorphism from a (discrete) group G t
 o Out(A)\, the outer automorphism group of a C*-algebra A. There are cohom
 ological obstructions to lifting such a G-kernel to a group action. In the
  setting of von Neumann algebras\, G-kernels on the hyperfinite II1-factor
  have been completely understood via deep results of Connes\, Jones and Oc
 neanu. In the talk I will explain how G-kernels on C*-algebras and the lif
 ting obstructions can be interpreted in terms cohomology with coefficients
  in crossed modules. G-kernels\, group actions and cocycle actions then gi
 ve rise to induced maps on classifying spaces. For strongly self-absorbing
  C*-algebras these classifying spaces turn out to be infinite loop spaces 
 creating a bridge to stable homotopy theory. Not only does this make the i
 nvariants computable\, it also gives rise to equivariant refinements. The 
 first part is a joint project with S. Giron Pacheco and M. Izumi\, the sec
 ond with my PhD student V. Bianchi.
LOCATION:Seminar Room 1\, Newton Institute
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