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SUMMARY:Topological Invariants for G-kernels and Group Actions - Ulrich Pe
 nnig (Cardiff University)
DTSTART:20250715T133000Z
DTEND:20250715T141000Z
UID:TALK233056@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 II_1-facto
 r have been completely understood via deep results of Connes\, Jones and O
 cneanu. In the talk I will explain how G-kernels on C*-algebras and the li
 fting obstructions can be interpreted in terms cohomology with coefficient
 s in crossed modules. G-kernels\, group actions and cocycle actions then g
 ive rise to induced maps on classifying spaces. For strongly self-absorbin
 g C*-algebras these classifying spaces turn out to be infinite loop spaces
  creating a bridge to stable homotopy theory.The talk is based on joint wo
 rk with S. Giron Pacheco and M. Izumi\, and with my PhD student V. Bianchi
 .
LOCATION:External
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