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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Fall 2023 • Question 5

Question

Math 6520 • Algebraic Topology Fall 2023 • Question 5

Let \(M\) be a closed, orientable 5-manifold with \(H_1(M) = \mathbb {Z} \oplus \mathbb {Z}_5\) and \(H_2(M) = \mathbb {Z}_2\). Find \(H_i(M)\) and \(H^i(M;\mathbb {Z})\) for all \(i \ge 0\).

Raw LaTeX

Let \(M\) be a closed, orientable 5-manifold with \(H_1(M) = \mathbb{Z} \oplus \mathbb{Z}_5\) and
\(H_2(M) = \mathbb{Z}_2\). Find \(H_i(M)\) and \(H^i(M;\mathbb{Z})\) for all \(i \ge 0\).

Topic Tags

Cohomology and Cup Products Fundamental Groups Homology with Coefficients