Infinite loop spaces and the Steenrod algebra

Haynes Miller
Tuesday, July 23, 2013 - from 09:30 to 10:30
There is a rather obvious spectral sequence converging to the cohomology of the zero-space of a connective spectrum, whose $E_2$ term is determined homologically from the spectrum cohomology as a module over the Steenrod algebra. I will describe joint work with Rune Haugseng in which we explore the computation of this $E_2$ term. We use simplicial methods with which Eilenberg and Mac Lane would have been comfortable. I will also report on current work which seeks to extend this to finite loop spaces, providing a context for my work with John Harper, from the 1980's, on looping spaces whose cohomology is of the form $U(M)$.