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On realizing diagrams of Π–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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Abstract
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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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Keywords
realization of diagrams, (simplicial)
Π–algebras, (resolution) model categories,
cohomology
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Mathematical Subject Classification
Primary: 18G55
Secondary: 55P65, 55Q05
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Publication
Received: 20 October 2005
Revised: 5 April 2006
Accepted: 5 April 2006
Published: 21 June 2006
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