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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2022 • Question 1

Question

Math 6510 • Differentiable Manifolds Spring 2022 • Question 1

Let \(X\subset \mathbb {R}^3\) be a smoothly embedded torus. Show that there is a plane \(P\subset \mathbb {R}^3\) such that \(X\cap P\) is a nonempty collection of circles.

Raw LaTeX

Let \(X\subset\mathbb{R}^3\) be a smoothly embedded torus. Show that there is a plane
\(P\subset\mathbb{R}^3\) such that \(X\cap P\) is a nonempty collection of circles.

Topic Tags

Smooth Manifolds and Embedded Submanifolds