Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-134/1/a/solution

For a finite graph , its Right-angled Artin group is
Its Salvetti complex is the one-vertex cube complex with an oriented loop labelled for each vertex of , a square torus for every edge, and more generally one cubulated -torus for every -clique, attached compatibly along coordinate subtori. Thus . The vertex link of a Salvetti complex is flag, so is a nonpositively curved cube complex.

New to topics? Read the docs here!