Hatcher-Algebraic-Topology · Problem 1.3.17

The Fundamental Group

Mathematics — Graph Theory · covering-spaces

Problem

Given a group GG and a normal subgroup NN, show that there exists a normal covering space X~→X\tilde{X} \to X with π1(X)≈G\pi_1(X) \approx G, π1(X~)≈N\pi_1(\tilde{X}) \approx N, and deck transformation group G(X~)≈G/NG(\tilde{X}) \approx G/N.

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