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Publication# Modèles tordus d'espaces de lacets libres et fonctionnels

Abstract

In this PhD thesis, we construct an explicit algebraic model over Z of the cochains of the free loop space of a 1-connected space X. We start from an enriched Adams-Hilton model of X, which can be obtained relatively easily when X is the realisation of a simplicial set. Note it is not supposed that the Steenrod algebra acts trivially on X. The second part is dedicated to the construction of a model of the cochains of mapping spaces XY. where X is r-connected and Y is a CW-complex that has dimension less or equal to r. The space X must possess commutative models for the cochains of each Ωk X for k ≤ r. We first construct an algebraic model for the cochains of XSn ∀n ≤ r, then we then glue all of them to obtain a model of the cochains of XY. We give examples for each of these situations. The techniques used here rely heavily on the concept of a twisted bimodule. A description of this can be found in [DH99b].

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Thesis

A thesis (: theses), or dissertation (abbreviated diss.), is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and

General algebraic modeling system

The general algebraic modeling system (GAMS) is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimizatio

Space

Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it,

If X is a simply connected space of finite type, then the rational homotopy groups of the based loop space of X possess the structure of a graded Lie algebra, denoted L-x. The radical of L-x, which is an important rational homotopy invariant of X, is of finite total dimension if the Lusternik-Schnirelmann category of X is finite. Let X be a simply connected space with finite Lusternik-Schnirelmann category. If dim L-x < infinity, i.e., if X is elliptic, then L-x is its own radical, and therefore the total dimension of the radical of L-x in odd degrees is less than or equal to its total dimension in even degrees (Friedlander and Halperin (1979) [8]). Felix conjectured that this inequality should hold for all simply connected spaces with finite Lusternik-Schnirelmann category. We prove Felix's conjecture in some interesting special cases, then provide a counter-example to the general case. (C) 2010 Elsevier B.V. All rights reserved.