Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2008 • Question 2

Question

Math 6510 • Differentiable Manifolds Fall 2008 • Question 2

Let \(G\) be a finite group that acts smoothly, and freely (without fixed points) on a manifold \(M\). Prove that the orbit space \(M/G\) admits a smooth structure (that is, has the structure of a smooth manifold).

Raw LaTeX

Let \(G\) be a finite group that acts smoothly, and freely (without fixed
points) on a manifold \(M\). Prove that the orbit space \(M/G\) admits a smooth
structure (that is, has the structure of a smooth manifold).

Topic Tags

Fixed Point Theorems and Borsuk-Ulam Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds