Algebraic & Geometric Topology 6 (2006) 763–807

DOI: 10.2140/agt.2006.6.763

arXiv: math.AT/0604161

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 in [J Pure Appl Alg. 103 (1995) 167-188] and [Topology 43 (2004) 857-892] 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.

Keywords

realization of diagrams, (simplicial) Π–algebras, (resolution) model categories, cohomology

Mathematical Subject Classification

Primary: 18G55

Secondary: 55P65, 55Q05

References

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Publication

Received: 20 October 2005
Revised: 5 April 2006
Accepted: 5 April 2006
Published: 21 June 2006

Authors