Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2003 • Question 1

Question

Math 6510 • Differentiable Manifolds Fall 2003 • Question 1

Let \(X\) and \(Y\) be closed submanifolds of \(\mathbb {R}^n\). Show that for almost all \(a\in \mathbb {R}^n\) the translate \(X+a=\{x+a\mid x\in X\}\) intersects \(Y\) transversally.

Raw LaTeX

Let \(X\) and \(Y\) be closed submanifolds of \(\mathbb{R}^n\). Show that for almost
all \(a\in\mathbb{R}^n\) the translate
\(X+a=\{x+a\mid x\in X\}\) intersects \(Y\) transversally.

Topic Tags

Smooth Manifolds and Embedded Submanifolds Transversality and Intersection Theory