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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2010 • Question 6

Question

Math 6510 • Differentiable Manifolds Spring 2010 • Question 6

Let \(f:S^2\to S^2\) be smooth and surjective. Prove that there is an open set \(U\subseteq S^2\) such that \(f:U\to f(U)\) is a diffeomorphism.

Raw LaTeX

Let \(f:S^2\to S^2\) be smooth and surjective. Prove that there is an open
set \(U\subseteq S^2\) such that \(f:U\to f(U)\) is a diffeomorphism.

Topic Tags

Diffeomorphisms and Isotopy Methods Fixed Point Theorems and Borsuk-Ulam