Hatcher-Algebraic-Topology · Problem 1.3.6

The Fundamental Group

Mathematics — Graph Theory · covering-spaces

Problem

Let XX be the shrinking wedge of circles in Example 1.25, and let X~\tilde{X} be its covering space shown in the figure below. Construct a two-sheeted covering space Y→X~Y \to \tilde{X} such that the composition Y→X~→XY \to \tilde{X} \to X of the two covering spaces is not a covering space. Note that a composition of two covering spaces does have the unique path lifting property, however.

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