Cell attachment
= Cell attachment
{title2=$X\cup_\phi D^q$}
Attaching a $q$-cell along $\phi:S^{q-1}\to X$ forms the quotient of $X\sqcup D^q$ identifying each boundary point with its image under $\phi$. A constant attaching map gives $X\vee S^q$. An attaching map can affect the <cohomology ring> even when it does not change the additive cohomology groups.