this talk will build on nitu$^\prime$'s talk to give some of the homotopy theory used in the madsen-weiss paper about the cohomology of the stable mapping class group $\gamma_{\infty, 1+1}$. i will tell you about quillen's plus construction and about operads as a recognition principle for infinite loop spaces, as well as at least hint at how they will be used in tillmann's proof that ${\bf z}\times{b}\gamma_{\infty,1+1}^+$ is an infinite loop space.