## On realizing diagrams of Π–algebras (2006)

### BibTeX

@MISC{Blanc06onrealizing,

author = {David Blanc and Mark W Johnson and James M Turner},

title = { On realizing diagrams of Π–algebras},

year = {2006}

}

### OpenURL

### Abstract

Given a diagram of Π–algebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulated in terms of generalized Π–algebras. This extends a program begun by Dwyer, Kan, Stover, Blanc and Goerss [21, 10] to study the realization of a single Π–algebra. In particular, we explicitly analyze the simple case of a single map, and provide a detailed example, illustrating the connections to higher homotopy operations.