Hatcher-Algebraic-Topology · Problem 4.1.5

Homotopy Theory

Mathematics — Graph Theory · relative-homotopy-groups

Problem

For a pair (X,A)(X, A) of path-connected spaces, show that π1(X,A,x0)\pi_1(X, A, x_0) can be identified in a natural way with the set of cosets HαH\alpha of the subgroup H⊂π1(X,x0)H \subset \pi_1(X, x_0) represented by loops in AA at x0x_0.

Related theory

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