On the cohomology algebra of free loop spaces

Let $X$ be a simply connected space and $\Bbb K$ be any field. The normalized singular cochains $N^*(X; {\Bbb K})$ admit a natural strongly homotopy commutative algebra structure, which induces a natural product on the Hochschild homology $HH_* N^*X$ of the space $X$. We prove that, endowed with this product, $HH_*N^*X$ is isomorphic to the cohomology algebra of the free loop space of $X$ with coefficients in $\Bbb K$. We also show how to construct a simpler Hochschild complex which allows direct computation.Comment: 21 pages, to appear in Topolog

Alge`bres de cochaiˆnes quasi-commutatives et fibrations alge´briques

AbstractLetk be a field of any characteristicp andk-dga the category of connected cochain algebras. In [3] Dupont and Hess defined notions of twisted tensor product, twisted extension, algebraic fibration and acyclic closure. In this paper we define the notion of quasi-commutative cochain algebras and their morphisms and we prove that every morphism of quasi-commutative cochain algebras is an algebraic fibration. Consequently, every such a cochain algebra admits an acyclic closure

United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS INERTIA AND TWISTED TENSOR PRODUCTS

IC/97/80 We prove in this note that twisted tensor products of free graded algebras as usually constructed can be viewed as quotients of free graded algebras by inert ideals. Permanent address

Hochschild cohomology of a strongly homotopy commutative algebra

The Hochschild cohomology of a DG algebra A with coefficients in itself is, up to a suspension of degrees, a graded Lie algebra. The purpose of this paper is to prove that a certain DG Lie algebra of derivations appears as a finite codimensional graded sub Lie algebra of this Lie algebra when A is a strongly homotopy commutative algebra whose homology is concentrated in finitely many degrees. This result has interesting implications for the free the loop space homology which we explore here as well. © 2013 Springer-Verlag Berlin Heidelberg

Les propriétés homologiques des algèbres elliptiques de petite dimension

Cette thèse est consacrée à l'étude des propriétés homologiques d'une famille d'algèbres associatives attachée aux courbes elliptiques. Chaque algèbre de cette famille admet un nombre ni de générateurs subordonnés aux relations quadratiques. Elles sont aujourd'hui connues sous le nom d'algèbres elliptiques de Sklyanin-Odesskii- Feigin. Il convient toutefois de souligner que le cas le plus simple, la famille d'algèbres elliptiques avec trois générateurs, était déjà connue de Artin et Shelter.This thesis is dedicated to the study of the homologiques properties of a family of associative algebras attached to the elliptic curves. Every algebra of this family admits a number nor of generators subordinate to the quadratiques relations. They are known under the name of elliptic algebras of Sklyanin-Odesskii-Feigin today. It is however advisable to underline that the simplest case, the family of elliptic algebras with three generators, was already known of Artin and Shelter.ANGERS-BU Lettres et Sciences (490072106) / SudocSudocFranceF