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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2010 • Question 5

Question

Math 6510 • Differentiable Manifolds Spring 2010 • Question 5

Let \(G\) be a Lie group with a discrete subgroup \(\Gamma \leq G\). Prove that \(\Gamma \) acts freely and properly discontinuously on \(G\). (It will follow that \(\Gamma \backslash G\) is a smooth manifold, but you don’t have to show this.)

Raw LaTeX

Let \(G\) be a Lie group with a discrete subgroup \(\Gamma\leq G\). Prove that
\(\Gamma\) acts freely and properly discontinuously on \(G\). (It will follow that
\(\Gamma\backslash G\) is a smooth manifold, but you don't have to show this.)

Topic Tags

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