Classifying spaces for proper group actions (Ex)

1. Let $D_{\infty} = \Zz \rtimes \Zz/2 = \Zz/2 \ast \Zz/2$$<wikitex>; # Let $D_{\infty} = \Zz \rtimes \Zz/2 = \Zz/2 \ast \Zz/2$ be the infinite dihedral group. Show that $\Rr$ with the obvious $D_{\infty}$-action is a model for $\underline{E}D_{\infty}$; see [[Classifying spaces for families of subgroups]]. # Find nice models for $\underline{E} SL_2(\Zz)$. </wikitex> == References == {{#RefList:}} [[Category:Exercises]] [[Category:Exercises without solution]]D_{\infty} = \Zz \rtimes \Zz/2 = \Zz/2 \ast \Zz/2$ be the infinite dihedral group. Show that $\Rr$$\Rr$ with the obvious $D_{\infty}$$D_{\infty}$-action is a model for $\underline{E}D_{\infty}$$\underline{E}D_{\infty}$; see Classifying spaces for families of subgroups.
2. Find nice models for $\underline{E} SL_2(\Zz)$$\underline{E} SL_2(\Zz)$.