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.

中文翻译：

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$E_{2}$ - 单元格和映射类组

我们证明了一种新的稳定结果，即“二级同调稳定性”，用于具有一个边界分量的可定向表面的映射类群的同源性。这些结果是通过在\(E_{2}\)代数类别中构造这些群的分类空间的 CW 近似来获得的，在特定消失线下方没有\(E_{2}\)元胞。