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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2017 • Question 6

Question

Math 6510 • Differentiable Manifolds Summer 2017 • Question 6

Let \(G\) be a Lie group. Prove that \(G\) is orientable, and that if \(L_g\in \operatorname {Diff}(G)\) is left multiplication by \(g\in G\), then \(L_g\) preserves orientation.

Raw LaTeX

Let \(G\) be a Lie group. Prove that \(G\) is orientable, and that if
\(L_g\in\operatorname{Diff}(G)\) is left multiplication by \(g\in G\), then \(L_g\)
preserves orientation.

Topic Tags

Lie Groups and Matrix Lie Groups Orientability and Volume Forms