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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2011 • Question 6

Question

Math 6510 • Differentiable Manifolds Spring 2011 • Question 6

Suppose that \(X\) and \(Y\) are two connected manifolds or cell complexes homotopy equivalent to each other. Prove that their universal covers \(\widetilde {X}\) and \(\widetilde {Y}\) are homotopy equivalent to each other. Carefully state all theorems you are using.

Raw LaTeX

Suppose that \(X\) and \(Y\) are two connected manifolds or cell complexes
homotopy equivalent to each other. Prove that their universal covers
\(\widetilde{X}\) and \(\widetilde{Y}\) are homotopy equivalent to each other.
Carefully state all theorems you are using.

Topic Tags

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