Algebraic Topology · Problem 4.1.6

Homotopy Theory — Allen Hatcher

Mathematics — Topology · relative-homotopy-groups-covering-spaces

Problem

If p:(X~,A~,x~0)→(X,A,x0)p: (\tilde{X}, \tilde{A}, \tilde{x}_0) \to (X, A, x_0) is a covering space with A~=p−1(A)\tilde{A} = p^{-1}(A), show that the map p∗:πn(X~,A~,x~0)→πn(X,A,x0)p_*: \pi_n(\tilde{X}, \tilde{A}, \tilde{x}_0) \to \pi_n(X, A, x_0) is an isomorphism for all n>1n > 1.

Related theory

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