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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2001 • Question 12

Question

Math 6510 • Differentiable Manifolds Fall 2001 • Question 12

Let \(M\) be a closed connected 7-manifold such that \(H_1(M;\mathbb {Z})=0\), \(H_2(M;\mathbb {Z})=\mathbb {Z}\), \(H_3(M;\mathbb {Z})=\mathbb {Z}/2\). Compute \(H_i(M;\mathbb {Z})\) and \(H^i(M;\mathbb {Z})\) for all \(i\).

Raw LaTeX

Let \(M\) be a closed connected 7-manifold such that
\(H_1(M;\mathbb{Z})=0\), \(H_2(M;\mathbb{Z})=\mathbb{Z}\),
\(H_3(M;\mathbb{Z})=\mathbb{Z}/2\). Compute \(H_i(M;\mathbb{Z})\) and
\(H^i(M;\mathbb{Z})\) for all \(i\).

Topic Tags

Cohomology and Cup Products Fundamental Groups Homology with Coefficients Homotopy and Degree on Manifolds