On realizing diagrams of Π–algebras

Blanc, David¹ ; Johnson, Mark W² ; Turner, James M³

¹Department of Mathematics, University of Haifa, 31905 Haifa, Israel
²Department of Mathematics, Penn State Altoona, Altoona PA 16601, USA
³Department of Mathematics, Calvin College, Grand Rapids MI 49546, USA

Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 763-807

Résumé

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.

Détail

DOI : 10.2140/agt.2006.6.763

Keywords: realization of diagrams, (simplicial) $\Pi$–algebras, (resolution) model categories, cohomology

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