CAT(k) group

A CAT(k) group is a type of geometric group that arises in the study of metric spaces and their large-scale geometric properties. The term "CAT(k)" comes from the work of mathematician Mikhail Gromov and relates to CAT(0) spaces, which are simply connected spaces that have non-positive curvature in a very generalized sense. In this context, a **CAT(k)** space is a geodesic metric space that satisfies a condition related to triangles.