Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Summer 2021 • Question 2

Question

Math 6520 • Algebraic Topology Summer 2021 • Question 2

Let \(p : \tilde {X} \to X\) be a covering map between two connected CW-complexes. If \(p\) is null-homotopic, prove that \(\tilde {X}\) is contractible. If you use a theorem make sure you state it carefully and include all the hypotheses.

Raw LaTeX

Let \(p : \tilde{X} \to X\) be a covering map between two connected CW-complexes.
If \(p\) is null-homotopic, prove that \(\tilde{X}\) is contractible. If you use a theorem
make sure you state it carefully and include all the hypotheses.

Topic Tags

CW Complexes and Cell Attachments Chain Complexes and Chain Homotopy Covering Spaces Homotopy Equivalence, Retracts, and Contractibility