Algebraic Topology
《Algebraic Topology》 · 第 374 页 · Section 4.1
For a CW complex \(X\) and a perfect normal subgroup \(N\triangleleft\pi_1(X)\), the plus construction gives a map \(X\to X^+\) inducing \(\pi_1(X^+)\cong\pi_1(X)/N\) while preserving homology with local coefficients pulled back from \(X^+\).