Sorin Popa (UCLA) : "On the vanishing cohomology problem for cocycle actions of groups on II$_1$ factors"

mercredi 4 juil. 2018, 14:00 → 15:00 Europe/Paris

I will present a result showing that any free cocycle action of a countable amenable group Gamma on any II_1 factor N can be perturbed by inner automorphisms to a genuine action. Besides containing all amenable groups, this vanishing cohomology property, called VC, is also closed to free products with amalgamation over finite groups. While no other examples of VC-groups are known, by considering special cocycle actions Gamma acting on N in the case N=R, N=L(F_infty), one can be exclude many groups from being VC. I will also discuss approximate versions of vanishing cohomology and explain a connection with Connes’ Approximate Embedding conjecture.