$E_2$-cells and mapping class groups

Abstract

We prove a new kind of stabilisation result, "secondary homological stability", for the homology of mapping class groups of orientable surfaces with one boundary component. These results are obtained by constructing CW approximations to the classifying spaces of these groups, in the category of $E_2$-algebras, which have no $E_2$-cells below a certain vanishing line.

v2: Final version, to appear in Publ. Math. Inst. Hautes Études Sci