Topological Invariants for G-kernels and Group Actions

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• Ulrich Pennig (Cardiff University)
• Tuesday 15 July 2025, 14:30-15:10
• External.

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TGAW02 - C*-algebras: classification and dynamical constructions

A G -kernel is a group homomorphism from a (discrete) group G to Out(A), the outer automorphism group of a C-algebra A. There are cohomological 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-factor have been completely understood via deep results of Connes, Jones and Ocneanu. In the talk I will explain how G-kernels on C-algebras and the lifting obstructions can be interpreted in terms cohomology with coefficients in crossed modules. G-kernels, group actions and cocycle actions then give 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.The talk is based on joint work with S. Giron Pacheco and M. Izumi, and with my PhD student V. Bianchi.

This talk is part of the Isaac Newton Institute Seminar Series series.

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