Yves Félix

Adams Cobar Equivalence

Let F be the homotopy fibre of a continuous map Y --> omega X, with X simply connected. We modify and extend a construction of Adams to obtain equivalences of DGAs and DGA modules, OMEGA-C*(X) --> congruent-to CU*(OMEGA-X), and OMEGA(C*omega(Y); C*(X)) --> congruent-to CU*(F), where on the left-hand side OMEGA(-) denotes the cobar construction. Our equivalences are natural in X and omega. Using this result we show how to read off the algebra H*(OMEGA-X; R) and the H*(OMEGA-X; R) module, H*(F; R), from free models for the singular cochain algebras CS*(X) and CS*(Y); here we assume R is a principal ideal domain and X and Y are of finite R type.

The Homotopy Lie-algebra for Finite Complexes

© Publications mathématiques de l’I.H.É.S., 1982, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Rational string topology

We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a 1-connected closed manifold

The rational LS category of products and of Poincare duality complexes

M

The Radius of Convergence of Poincaré Series of Loop Spaces.

. We prove that the loop homology of

Rational homotopy of the polyhedral product functor

M

Formal Spaces With Finite-dimensional Rational Homotopy

is isomorphic to the Hochschild cohomology of the cochain algebra

Lie Models for the Components of Sections of a Nilpotent Fibration

C^\ast(M)

Rational Betti numbers of configuration spaces

with coefficients in itself. Some explicit computations of the loop product and the string bracket are given.

Rational homotopy of gauge groups

We give a new characterisation of rational LS category, cat(o)(X), from which two theorems follow. Theorem 1: cat(o)(X + Y) = cat(o)(X) + cat(o)(Y). Theorem 3: If X is a Poincare: duality complex, then cat(o)(X) = e(o)(X), where e(o) is Toomers invariant