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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2006 • Question 12

Question

Math 6510 • Differentiable Manifolds Fall 2006 • Question 12

Let \(X\) be the quotient space of the 2-sphere \(S^2\) under the identifications \(x\sim -x\) for \(x\) in the equator \(S^1\). Compute the homology groups \(H_i(X)\) using any method you like.

Raw LaTeX

Let \(X\) be the quotient space of the 2-sphere \(S^2\) under the identifications
\(x\sim -x\) for \(x\) in the equator \(S^1\). Compute the homology groups \(H_i(X)\) using any
method you like.

Topic Tags

Cellular Homology Homology with Coefficients Relative Homology and Long Exact Sequences