On the Third-Degree Continuous Cohomology of Simple Lie Groups

Abstract

We show that the class of connected, simple Lie groups that have non-vanishing third-degree continuous cohomology with trivial $\mathbb{R}$-coefficients consists precisely of all simple complex Lie groups and of $\widetilde{{\mathrm{SL}}_2(\mathbb{R})}$.

9 pages, comments are welcome