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Let (X, ∗) be a pointed CW-complex, K be a simplicial complex on n vertices and X K be the associated polyhedral power. In this paper, we construct a Sullivan model of X K from K and from a model of X. Let F(K, X) be the homotopy fiber of the inclusion X K → X n. Recent results of Grbić and Theriault, on one side, and of Denham and Suciu, on the other side, show the diversity of the possible homotopy types for F(K, X). Here, we prove that the corresponding map between Sullivan models is Golod attached, generalizing a result of J. Backelin. This property is deduced from the existence of a succession of fibrations whose fibers are suspensions. We consider also the Lusternik-Schnirelmann category of X K.Inthecase that cat X n = n cat X, we prove that cat X K =(catX)(1 + dim K). Finally, we mention that this work is written in the case of a sequence of pairs, X =(Xi,Ai)1≤i≤n, as in a recent work of Bahri, Bendersky, Cohen and Gitler

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Yi, where Yi

Year: 2008

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oai:CiteSeerX.psu:10.1.1.193.3750

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