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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2007 • Question 12

Question

Math 6510 • Differentiable Manifolds Winter 2007 • Question 12

Let \(M\) be a closed connected 5-manifold such that \(\pi _1(M)\cong \mathbb {Z}/7\). If \(H_2(M;\mathbb {Z})\cong \mathbb {Z}\), compute all other homology and cohomology groups of \(M\) with integral coefficients.

Raw LaTeX

Let \(M\) be a closed connected 5-manifold such that \(\pi_1(M)\cong\mathbb{Z}/7\).
If \(H_2(M;\mathbb{Z})\cong\mathbb{Z}\), compute all other homology and cohomology groups
of \(M\) with integral coefficients.

Topic Tags

Cohomology and Cup Products Fundamental Groups Homology with Coefficients Homotopy Groups