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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2007 • Question 8

Question

Math 6510 • Differentiable Manifolds Winter 2007 • Question 8

Show that for any two points \(x,y\in \mathbb {R}^n\) there is a compactly supported isotopy \(\phi _t\) (i.e. it is identity outside a compact set) such that \(\phi _0=id\) and \(\phi _1(x)=y\).

Raw LaTeX

Show that for any two points \(x,y\in\mathbb{R}^n\) there is a compactly supported
isotopy \(\phi_t\) (i.e. it is identity outside a compact set) such that \(\phi_0=id\) and
\(\phi_1(x)=y\).

Topic Tags

Compactly Supported Forms and Integration Diffeomorphisms and Isotopy Methods Fundamental Groups