Unformatted text preview: v x ) || = 1 } be the circle bundle of S 2 . Prove that Q ( S 2 ) is a submanifold of T S 2 of dimension three. 4. Let ρ : R × S n → S n and σ : R n +1 × S n → S n be trivial vector bundles. Show that T S n ⊕ ( R × S n ) ∼ = ( R n +1 × S n ) . Hint: Realize ρ as the vector bundle whose one-dimensional ﬁber is the normal to the sphere. 5. Submit a one-page introduction to the topic of your project (e.g. motivation, description of the system and setting, relation to the material in the course). 1...
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- Spring '10
- Vector Space, Manifold, normed vector space, Tangent bundle, trivial vector bundles