 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-4/21h/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Let

i : L ↪ M

j : L ↪ N

r : M ↪ K

, and

s : N ↪ K

\dots ⟶ H_{k} (L) (i_{*}, - j_{*}) H_{k} (M) \oplus H_{k} (N) r_{*} + s_{*} H_{k} (K) \partial_{*} H_{k - 1} (L) ⟶ \dots .

The same sequence continues through degree zero, or uniformly in all degrees when written with reduced homology.

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