Hatcher-Algebraic-Topology · Problem 4.1.2

Homotopy Theory

Mathematics — Graph Theory · homotopy-groups-functoriality

Problem

Show that if φ:X→Y\varphi : X \to Y is a homotopy equivalence, then the induced homomorphisms φ∗:πn(X,x0)→πn(Y,φ(x0))\varphi_* : \pi_n(X, x_0) \to \pi_n(Y, \varphi(x_0)) are isomorphisms for all nn. [The case n=1n = 1 is Proposition 1.18.]

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