Equivariant maps (Ex)

Let $G$$<wikitex>; Let $G$ be a finite group, e.g. $G = \Zz/2$. Find two spaces $X$ and $Y$ with a $G$-action and an equivariant map $f \co X \ra Y$ such that $$ X^{G} \; \textup{is not homotopy equivalent to} \; Y^{G}.$$ </wikitex> == References== {{#RefList:}} [[Category:Exercises]] [[Category:Exercises with solution]]G$ be a finite group, e.g. $G = \Zz/2$$G = \Zz/2$. Find two spaces $X$$X$ and $Y$$Y$ with a $G$$G$-action and an equivariant map

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$f \co X \ra Y$ such that

$\displaystyle X^{G} \; \textup{is not homotopy equivalent to} \; Y^{G}.$ $$\displaystyle X^{G} \; \textup{is not homotopy equivalent to} \; Y^{G}.$$