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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2017 • Question 2

Question

Math 6510 • Differentiable Manifolds Summer 2017 • Question 2

Let \(\Sigma _g\) be a closed, orientable surface of genus \(g\), and let \(T\Sigma _g\) be its tangent bundle. Prove that \(T\Sigma _g\) is trivial if and only if \(g=1\).

Raw LaTeX

Let \(\Sigma_g\) be a closed, orientable surface of genus \(g\), and let
\(T\Sigma_g\) be its tangent bundle. Prove that \(T\Sigma_g\) is trivial if and only
if \(g=1\).

Topic Tags

Orientability and Volume Forms Smooth Manifolds and Embedded Submanifolds Surface Topology and Surface Groups Tangent Bundles and Vector Bundles