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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2016 • Question 9

Question

Math 6510 • Differentiable Manifolds Summer 2016 • Question 9

Define the singular homology groups \(H_i(X;\mathbb {Z})\) of a topological space \(X\) and compute the singular homology groups of the \(n\)-sphere \(S^n\), justifying all your steps.

Raw LaTeX

Define the singular homology groups \(H_i(X;\Z)\) of a topological space
\(X\) and compute the singular homology groups of the \(n\)-sphere \(S^n\), justifying
all your steps.

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Topic Tags

Cellular Homology Homology with Coefficients Point-Set Topology and Separation Theorems Relative Homology and Long Exact Sequences