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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2021 • Question 4

Question

Math 6510 • Differentiable Manifolds Fall 2021 • Question 4

Let \(X\) and \(Y\) be closed sub-manifolds 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 sub-manifolds 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

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