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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2007 • Question 15

Question

Math 6510 • Differentiable Manifolds Winter 2007 • Question 15

Prove that the map \(h:S^3\to \mathbb {C}P^1\) given by \(h(x,y)=[x:y]\) is a fiber bundle. Here, \(S^3\) is the unit sphere \(|x|^2+|y|^2=1\) in \(\mathbb {C}^2\).

Raw LaTeX

Prove that the map \(h:S^3\to\mathbb{C}P^1\) given by \(h(x,y)=[x:y]\) is a fiber
bundle. Here, \(S^3\) is the unit sphere \(|x|^2+|y|^2=1\) in \(\mathbb{C}^2\).

Topic Tags

Tangent Bundles and Vector Bundles