Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2012 • Question 1

Question

Math 6510 • Differentiable Manifolds Spring 2012 • Question 1

Show that \(\mathrm {SL}_n(\mathbb {R})\) is a manifold, and that it is a Lie group. (Do not use the theorem that any closed subgroup of a Lie group is a Lie group.)

Raw LaTeX

Show that \(\SL_n(\R)\) is a manifold, and that it is a Lie group. (Do not
use the theorem that any closed subgroup of a Lie group is a Lie group.)

Topic Tags

Homotopy and Degree on Manifolds Lie Groups and Matrix Lie Groups Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds