On the first continuous $L^2$-cohomology of free group factors

Abstract

We prove that the first continuous $L^2$-cohomology of free group factors vanishes. This answers a question by Andreas Thom regarding continuity properties of free difference quotients and shows that one can not distinguish free group factors by means of first continuous $L^2$-Betti number.

12 pages, corrected version

References in corpus (1)

• L^2-Homology for von Neumann Algebras

Cited by in corpus (2)

• Vanishing of the first continuous L^2-cohomology for II_1 factors
• $L^2$-homology for inclusions of von Neumann algebras