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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2013 • Question 11

Question

Math 6510 • Differentiable Manifolds Fall 2013 • Question 11

Let \(p:\widetilde {X}\to X\) be a covering map between cell complexes. Assume that \(\widetilde {X}\) is connected and that \(p\) is null-homotopic. Prove that \(\widetilde {X}\) is contractible.

Raw LaTeX

Let \(p:\widetilde{X}\to X\) be a covering map between cell complexes. Assume
that \(\widetilde{X}\) is connected and that \(p\) is null-homotopic. Prove that
\(\widetilde{X}\) is contractible.

Topic Tags

CW Complexes and Cell Attachments Covering Spaces Homotopy Equivalence, Retracts, and Contractibility Homotopy and Degree on Manifolds