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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2001 • Question 4

Question

Math 6510 • Differentiable Manifolds Fall 2001 • Question 4

  1. Give a definition of the tangent bundle \(TM\) of a manifold \(M\).
  2. Give a definition of what it means for a manifold to be orientable.
  3. Show that \(TM\), viewed as a differentiable manifold, is always orientable.

Raw LaTeX

\begin{enumerate}
\item Give a definition of the tangent bundle \(TM\) of a manifold \(M\).
\item Give a definition of what it means for a manifold to be orientable.
\item Show that \(TM\), viewed as a differentiable manifold, is always orientable.
\end{enumerate}

Topic Tags

Homotopy and Degree on Manifolds Orientability and Volume Forms Smooth Manifolds and Embedded Submanifolds Tangent Bundles and Vector Bundles