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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2017 • Question 10

Question

Math 6510 • Differentiable Manifolds Fall 2017 • Question 10

Let \(D^k\) be the closed \(k\)-dimensional disk. Use that \(D^k/\partial D^k=S^k\) to find \(H_n(S^k;\mathbb {Z})\) for all \(n\).

Raw LaTeX

Let \(D^k\) be the closed \(k\)-dimensional disk. Use that
\(D^k/\partial D^k=S^k\) to find \(H_n(S^k;\Z)\) for all \(n\).

Topic Tags

Homology with Coefficients