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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2012 • Question 8

Question

Math 6510 • Differentiable Manifolds Fall 2012 • Question 8

Let \(f:M\to N\) be a smooth map of smooth manifolds. If \(Q\subseteq N\) is an embedded submanifold, and \(f\) is transverse to \(Q\), prove that \(f^{-1}(Q)\) is a manifold.

Raw LaTeX

Let \(f:M\to N\) be a smooth map of smooth manifolds. If \(Q\subseteq N\) is an
embedded submanifold, and \(f\) is transverse to \(Q\), prove that \(f^{-1}(Q)\) is a
manifold.

Topic Tags

Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds Transversality and Intersection Theory