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On
realizing diagrams of $\Pi$–algebras
David Blanc, Mark W Johnson and James M Turner |
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Algebraic & Geometric Topology 6 (2006) 763–807
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arXiv: math.AT/0604161 |
Abstract |
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Given a diagram of –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 –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 –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) $\Pi$–algebras,
(resolution) model categories, cohomology
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Mathematical Subject Classification 2000
Primary: 18G55
Secondary: 55Q05, 55P65
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References |
Forward citations |
Publication
Received: 20 October 2005
Revised: 5 April 2006
Accepted: 5 April 2006
Published: 21 June 2006
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Authors |
| David Blanc | |
| Department of Mathematics University of Haifa 31905 Haifa Israel |
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| Mark W Johnson | |
| Department of Mathematics Penn State Altoona Altoona PA 16601 USA |
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| James M Turner | |
| Department of Mathematics Calvin College Grand Rapids MI 49546 USA |
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