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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1995 • Question 6

Question

Math 6510 • Differentiable Manifolds Fall 1995 • Question 6

Suppose that \(p:\widetilde {X}\to X\) is a covering map between connected manifolds. Prove that if \(p\) is null-homotopic, then \(\widetilde {X}\) is contractible.

Raw LaTeX

Suppose that \(p:\widetilde{X}\to X\) is a covering map between connected
manifolds. Prove that if \(p\) is null-homotopic, then \(\widetilde{X}\) is
contractible.

Topic Tags

Covering Spaces Homotopy Equivalence, Retracts, and Contractibility Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds