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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2004/iii/paper-16/3/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 16 / 3 / a / Solution by Codex 0 Created 2026-10-03 Updated 2026-10-14
This sequence cannot occur. Poincare duality and the universal coefficient theorem for cohomology imply
(1)
Thus a nonzero rank-two third homology group is incompatible with the proposed first homology group.
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