Hatcher-Algebraic-Topology · Problem 4.1.6

Homotopy Theory

Mathematics — Graph Theory · covering-spaces-relative-homotopy

Problem

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