The moduli space of topological realizations of an unstable coalgebra

George Raptis
Thursday, July 25, 2013 - from 16:30 to 16:55
The mod p homology of a space is an unstable coalgebra over the Steenrod algebra at the prime p. This talk will be about the problem of realizing an unstable coalgebra as the homology of a space. More generally, one can consider a moduli space of all such topological realizations and ask for a description of its homotopy type. Following methods introduced by Blanc, Dwyer and Goerss to study topological realizations of $\Pi$-algebras, I will present a description of the realization space of an unstable coalgebra in terms of its Andr\'{e}-Quillen cohomology. This description readily yields obstruction theories for the existence and uniqueness of realizations recovering and extending previously known results of Blanc, Bousfield and others. This is joint work with G. Biedermann and M. Stelzer.