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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2016 • Question 9

Question

Math 6510 • Differentiable Manifolds Fall 2016 • Question 9

Prove that \(H_i(S^2\vee S^4,\mathbb {Z})\) and \(H_i(\mathbb {C}P^2,\mathbb {Z})\) are isomorphic for all \(i\), but that \(S^2\vee S^4\) is not homotopy equivalent to \(\mathbb {C}P^2\).

Raw LaTeX

Prove that \(H_i(S^2\vee S^4,\Z)\) and \(H_i(\mathbb{C}P^2,\Z)\) are isomorphic
for all \(i\), but that \(S^2\vee S^4\) is not homotopy equivalent to
\(\mathbb{C}P^2\).

Topic Tags

Chain Complexes and Chain Homotopy Homology with Coefficients Homotopy Equivalence, Retracts, and Contractibility Homotopy and Degree on Manifolds