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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2004 • Question 5

Question

Math 6510 • Differentiable Manifolds Fall 2004 • Question 5

Let \(X\) and \(Y\) be two submanifolds of \(\mathbb {R}^n\). Show that for almost every \(a\in \mathbb {R}^n\) the translate \[ X+a=\{x+a\mid x\in X\} \] is transverse to \(Y\).

Raw LaTeX

Let \(X\) and \(Y\) be two submanifolds of \(\mathbb{R}^n\). Show that for almost every
\(a\in\mathbb{R}^n\) the translate
\[
  X+a=\{x+a\mid x\in X\}
\]
is transverse to \(Y\).

Topic Tags

Smooth Manifolds and Embedded Submanifolds Transversality and Intersection Theory