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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2020 • Question 11

Question

Math 6510 • Differentiable Manifolds Summer 2020 • Question 11

Suppose \(M\) is a closed connected orientable 5-manifold such that \(H_1(M)=\mathbb {Z}/2\mathbb {Z}\) and \(H_2(M)=\mathbb {Z}\oplus \mathbb {Z}/3\mathbb {Z}\). Compute \(H_i(M)\) and \(H^i(M)\) for all \(i\).

Raw LaTeX

Suppose \(M\) is a closed connected orientable 5-manifold such that
\(H_1(M)=\Z/2\Z\) and \(H_2(M)=\Z\oplus\Z/3\Z\). Compute \(H_i(M)\) and \(H^i(M)\) for
all \(i\).

Topic Tags

Cohomology and Cup Products Fundamental Groups Homology with Coefficients Orientability and Volume Forms