The mod 2 homology of infinite loopspaces (Q1948297)

This paper studies a spectral sequence for computing \(H^*(\Omega^{\infty}X; {\mathbb Z}_2)\), which arises from applying the mod \(2\) homology functor to the Goodwillie tower associated to the functor that maps a spectrum \(X\) to the suspension spectrum of its \(0\)-th space. The \(E^1\) page is the homology of the extended powers of \(X\), and has a rich structure -- it is a bigraded Hopf algebra, a right Steenrod module, and a left Dyer-Lashof module. The paper investigates the interaction of the spectral sequence with these structures.