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On realizing diagrams of Pi-algebras

David Blanc·Mark W Johnson·James M Turner
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Abstract

Given a diagram of Pi-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 Pi-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 Pi-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.

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David Blanc, Mark W Johnson, James M Turner. 2009-04-03. On realizing diagrams of Pi-algebras. https://doi.org/10.2140/agt.2006.6.763

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