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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Summer 2022 • Question 2

Question

Math 6520 • Algebraic Topology Summer 2022 • Question 2

Let \(f:M\to N\) be a covering map between manifolds that are both nonempty, connected, and compact without boundary. Suppose \(f\) is homotopic to a constant map. Prove that \(N\) is a point.

Raw LaTeX

Let \(f:M\to N\) be a covering map between manifolds that are both nonempty, connected, and compact without
boundary. Suppose \(f\) is homotopic to a constant map. Prove that \(N\) is a point.

Topic Tags

Classification of Covering Spaces Covering Spaces Free Groups, Graph Coverings, and Presentations Homotopy Equivalence, Retracts, and Contractibility