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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2018 • Question 2

Question

Math 6510 • Differentiable Manifolds Spring 2018 • Question 2

Let \(M\) and \(N\) be smooth manifolds of the same dimension, and suppose \(M\) is compact. Prove that if \(f:M\to N\) is an immersion then \(f^{-1}(y)\) is finite for any \(y\in N\).

Raw LaTeX

Let \(M\) and \(N\) be smooth manifolds of the same dimension, and suppose
\(M\) is compact. Prove that if \(f:M\to N\) is an immersion then \(f^{-1}(y)\) is
finite for any \(y\in N\).

Topic Tags

Homotopy and Degree on Manifolds Immersions, Submersions, and Embeddings Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds