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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2000 • Question 6

Question

Math 6510 • Differentiable Manifolds Fall 2000 • Question 6

A. Find an explicit CW complex structure for the complex projective space \(\mathbb {C}P^3\), and compute the singular homology groups (over \(\mathbb {Z}\)) using cellular homology.

B. Find an explicit CW complex structure for \(S^2\times S^4\), and compute the singular homology groups using cellular homology.

Raw LaTeX

\textbf{A.} Find an explicit CW complex structure for the complex projective space
\(\mathbb{C}P^3\), and compute the singular homology groups (over \(\mathbb{Z}\)) using
cellular homology.

\textbf{B.} Find an explicit CW complex structure for \(S^2\times S^4\), and compute the
singular homology groups using cellular homology.

Topic Tags

CW Complexes and Cell Attachments Cellular Homology Homology with Coefficients Real Projective Spaces