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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2007 • Question 7

Question

Math 6510 • Differentiable Manifolds Fall 2007 • Question 7

Prove that for any \(x,y\in \mathbb {R}^n\) there a compactly supported isotopy taking \(x\) to \(y\) (i.e. there is an isotopy \(f_t:\mathbb {R}^n\to \mathbb {R}^n\) such that \(f_0=\id \), \(f_1(x)=y\) and \(f_t=\id \) outside some ball).

Raw LaTeX

Prove that for any \(x,y\in\R^n\) there a compactly supported isotopy taking
\(x\) to \(y\) (i.e. there is an isotopy \(f_t:\R^n\to\R^n\) such that \(f_0=\id\),
\(f_1(x)=y\) and \(f_t=\id\) outside some ball).

Topic Tags

Compactly Supported Forms and Integration Diffeomorphisms and Isotopy Methods Fundamental Groups