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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2005 • Question 7

Question

Math 6510 • Differentiable Manifolds Winter 2005 • Question 7

Prove or give a counterexample (with proofs): If \(M\) is a closed submanifold of \(\mathbb {R}^n\) then its tangent bundle is trivial if and only if its normal bundle is trivial.

Raw LaTeX

Prove or give a counterexample (with proofs): If \(M\) is a closed submanifold of
\(\mathbb{R}^n\) then its tangent bundle is trivial if and only if its normal bundle is
trivial.

Topic Tags

Smooth Manifolds and Embedded Submanifolds Tangent Bundles and Vector Bundles