Let $f:K\to X$ be a map, with mapping cyliner $M=X\cup_{f}(K\times \{ 1\})$. We define $\pi_n (f)$ as $\pi_n (M,K\times \{ 1\})$. An element of $\pi_n (f)$ is represented by a pair of maps $\alpha :S^{n-1}\to K$ and $\beta :D^n \to X$ with $\beta |_{S^{n-1}}=f\circ \alpha$.

C.T.C. Wall in his paper "Finiteness conditions for CW-complexes" says that if $f:K\to X$ induces an isomorphism of fundamental groups (where $K$ is a finite bouquet of 1-spheres) and $\pi_2 (f)$ is a free $\mathbb{Z}\pi_1 (X)$-module, then we can attach a finite set of 2-cells to $K$, necessarily with trivial attaching maps. Is there someone who explains me why this happens? How if $\pi_2 (f)$ is a free $\mathbb{Z}\pi_1 (X)$-module, we can attach 2-cells to $K$, necessarily with trivial attaching maps?