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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