# Hatcher 0.25

Hatcher, Algebraic Topology, Chapter 0

25. If $X$ is a CW complex with components $X_\alpha$, show that the suspension $SX$ is homotopy equivalent to $Y\vee_\alpha SX_\alpha$ for some graph $Y$. In the case that $X$ is a finite graph, show that $SX$ is homotopy equivalent to a wedge sum of circles and 2-spheres.

Proof.

$\square$