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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2016 • Question 9

Question

Math 6510 • Differentiable Manifolds Spring 2016 • Question 9

Let \(X\) be a path connected space that is locally simply connected. Give the construction of \(p:\widetilde {X}\to X\), the universal cover of \(X\). You don’t have to define what a universal cover is, or show that your construction is a universal cover. Just state the description of the universal cover for \(X\) used in the standard proof that the universal cover for \(X\) exists.

Raw LaTeX

Let \(X\) be a path connected space that is locally simply connected. Give
the construction of \(p:\widetilde{X}\to X\), the universal cover of \(X\). You
don't have to define what a universal cover is, or show that your construction is
a universal cover. Just state the description of the universal cover for \(X\) used
in the standard proof that the universal cover for \(X\) exists.

Topic Tags

Covering Spaces Fundamental Groups Universal Coefficient Theorem