can anyone help me with this problem. thanx.
Show that there are cofiber sequence $S^{n+3} \to S^{n+2} \to \sum^{n}\mathbb{C}P^2$ for each $n \in \mathbb{Z}^+$. Conclude that a space of the form $S^{n+2} \bigcup_{\alpha}D^{n+4}$ is homotopy equivalent to either$\sum^{n}\mathbb{C}P^2$ or $ S^{n+2} \vee S^{n+4} $.
Hint: use the Steenrod operations. (Steenrod squares)