Location of Repository

RATIONAL HOMOTOPY OF THE POLYHEDRAL PRODUCT FUNCTOR

By Yves Félix and Daniel Tanré

Abstract

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

Topics: Yi, where Yi
Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.193.3750
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.ams.org/journals/pr... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.