Outer space
In their 1986 paper Culler and Vogtmann do not assign "Xn" a specific name. According to Vogtmann, the term "Outer space" for the complex "Xn" was later coined by Peter Shalen. In subsequent years the Outer space became a central object in the study of Out("F""n"). In particular, the Outer space has a natural compactification, similar to Thurston's compactification of the Teichmüller space, and studying the action of Out("F""n") on this compactification yields interesting information about dynamical properties of automorphisms of free groups.