A remark on the fundamental group of a compact negatively curved manifold

In this expository article we review some results about the fundamental group of a compact negatively curved manifold. In particular, a theorem of Gusevskij, see [7], it states that the fundamental group of a compact negatively curved manifold does not belong to C, where C is the smallest class of groups that contains all amenable groups and is closed under free products and finite extensions. The class C is quite natural and was introduced for the first time in [8].