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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2003 • Question 14

Question

Math 6510 • Differentiable Manifolds Fall 2003 • Question 14

Suppose \(M\) is a closed connected 5-manifold such that \(\pi _1(M)\cong \mathbb {Z}/3\mathbb {Z}\). If \(H_2(M;\mathbb {Z})\cong \mathbb {Z}\), compute all other homology and cohomology groups of \(M\) with integral coefficients.

Raw LaTeX

Suppose \(M\) is a closed connected 5-manifold such that
\(\pi_1(M)\cong\mathbb{Z}/3\mathbb{Z}\). 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