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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2008 • Question 1

Question

Math 6510 • Differentiable Manifolds Fall 2008 • Question 1

Let \(\mathrm {SL}(2,\mathbb {R})\) denote the subset of \(M^2\) (\(2\times 2\) real matrices), with determinant equal to one. Prove that \(\mathrm {SL}(2,\mathbb {R})\) is a regular submanifold of \(M^2=\mathbb {R}^4\), and find it’s dimension.

Raw LaTeX

Let \(\SL(2,\R)\) denote the subset of \(M^2\) (\(2\times2\) real matrices), with
determinant equal to one. Prove that \(\SL(2,\R)\) is a regular submanifold of
\(M^2=\R^4\), and find it's dimension.

Topic Tags

Lie Groups and Matrix Lie Groups Smooth Manifolds and Embedded Submanifolds