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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2020 • Question 2

Question

Math 6510 • Differentiable Manifolds Summer 2020 • Question 2

Let \(M^2\) be a smooth two manifold without boundary and \(i:M^2\to \mathbb {R}^5\) be a smooth immersion. Show that there is a projection \(\pi :\mathbb {R}^5\to \mathbb {R}^4\) such that \(\pi \circ i\) is an immersion.

Raw LaTeX

Let \(M^2\) be a smooth two manifold without boundary and \(i:M^2\to\R^5\) be
a smooth immersion. Show that there is a projection \(\pi:\R^5\to\R^4\) such that
\(\pi\circ i\) is an immersion.

Topic Tags

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