Applications of perturbation theory to iterated fibrations
type: Item
instance of: scholarly article
title: Applications of perturbation theory to iterated fibrations
zbMATH Open document ID: 0632.55011
DOI: 10.1007/BF01165893
author: Jim Stasheff
author: Larry A. Lambe
published in: Manuscripta Mathematica
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155226
review text: The purpose of this paper is to prove the following result. Given a tower of fibrations \[ X=E_ n\to E_{n-1}\to...\to E_ 0\to E_{-1}=* \] in which all of the fibrations \(F_ i\to E_ i\to E_{i-1}\) have simply connected torsion free homology \(H_*(F_ i;R)\) over a ring R, there is a differential \(\partial\) and a chain homotopy equivalence \[ f: C_*(X;R)\to M_ X=(H_*(F_ 0)\otimes_{R}H_*(F_ 1)\otimes_{R}...\otimes_{R}H_*(F_ n),\partial). \] Moreover, there is a homotopy associative coalgebra structure on \(M_ X\) such that f extends to a homotopy equivalence \(C_*(\Omega X;R)\to {\tilde \Omega}M_ X\) where \(\Omega\) X is the loop space of X and \({\tilde \Omega}\)M\({}_ X\) is the tilde-cobar construction in the sense of the second author [Trans. Am. Math. Soc. 108, 293-312 (1963; Zbl 0114.394)].
Mathematics Subject Classification ID: 55U15
Mathematics Subject Classification ID: 57T30
Mathematics Subject Classification ID: 57T35
Mathematics Subject Classification ID: 55R20
zbMATH DE Number: 4028415
zbMATH Keywords: tower of fibrations
zbMATH Keywords: chain homotopy equivalence
zbMATH Keywords: homotopy associative coalgebra structure
zbMATH Keywords: loop space
zbMATH Keywords: tilde-cobar construction
reviewed by: Jean-Claude Thomas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4028415