 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-3/20f/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Triangulate

X

and adjoin one new vertex joined to every simplex; the resulting simplicial complex realizes the cone

CX

. The cone contracts to its apex, so

H_{0} (CX) ≅ Z, H_{i} (CX) = 0 (i > 0) .

 New to topics? Read the docs here!