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2006 On realizing diagrams of $\Pi$–algebras
David Blanc, Mark W Johnson, James M Turner
Algebr. Geom. Topol. 6(2): 763-807 (2006). DOI: 10.2140/agt.2006.6.763

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.

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David Blanc. Mark W Johnson. James M Turner. "On realizing diagrams of $\Pi$–algebras." Algebr. Geom. Topol. 6 (2) 763 - 807, 2006. https://doi.org/10.2140/agt.2006.6.763

Information

Received: 20 October 2005; Revised: 5 April 2006; Accepted: 5 April 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1125.18011
MathSciNet: MR2240915
Digital Object Identifier: 10.2140/agt.2006.6.763

Subjects:
Primary: 18G55
Secondary: 55P65, 55Q05

Rights: Copyright © 2006 Mathematical Sciences Publishers

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