Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2006 • Question 3

Question

Math 6510 • Differentiable Manifolds Winter 2006 • Question 3

  1. Give a careful definition of the tangent bundle of a manifold \(X\).
  2. Show that the total space of the tangent bundle of \(S^2\) is not diffeomorphic to \(S^2\times \mathbb {R}^2\).

Raw LaTeX

\begin{enumerate}
\item Give a careful definition of the tangent bundle of a manifold \(X\).
\item Show that the total space of the tangent bundle of \(S^2\) is not diffeomorphic to
\(S^2\times\mathbb{R}^2\).
\end{enumerate}

Topic Tags

Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds Tangent Bundles and Vector Bundles