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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2018 • Question 9

Question

Math 6510 • Differentiable Manifolds Spring 2018 • Question 9

Let \(p:\widetilde {X}\to X\) be a cover of connected spaces. Prove \(p_*:\pi _1\widetilde {X}\to \pi _1X\) is injective.

Raw LaTeX

Let \(p:\widetilde{X}\to X\) be a cover of connected spaces. Prove
\(p_*:\pi_1\widetilde{X}\to\pi_1X\) is injective.

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Topic Tags

Covering Spaces Fundamental Groups Homotopy Groups