The overarching themes of this thesis are the algebraic structure of Hochschild complexes
and free loop spaces. It is a presentation of three projects in progress, followed by two …

We construct for any algebra over an operad an Hochschild chain complex. In the case of
the singular cochain complex of a topological space, considered as a commutative algebra …

A recent explosion of algebraic structures derived in quantum field theory [14, 15] and in the
theory of vertex operator algebras [13] has led to the renaissance of operads and algebras …

We give a general method for constructing explicit and natural operations on the Hochschild
complex of algebras over any prop with A∞-multiplication—we think of such algebras as …

A classical E-infinity operad is formed by the bar construction of the symmetric groups. Such
an operad has been introduced by M. Barratt and P. Eccles in the context of simplicial sets in …

We introduce two coloured operads in sets–the lattice path operad and a cyclic extension of
it–closely related to iterated loop spaces and to universal operations on cochains. As main …

The recent explosion of algebraic structures derived in quaaatum field theory [14, 15] and in
the theory of vertex operator algebras [13] has led to a renaissance of operads and algebras …

We construct a 2-colored operad Ger∞ which, on the one hand, extends the operad Ger∞
governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored …

The aim of this paper is to introduce the category of Hoch-algebras whose objects are
associative algebras equipped with an extra magmatic operation≻ verifying the following …

In this thesis natural operations on the (higher) Hochschild complex of a given family of
algebras are investigated. We give a description of all formal operations (in the sense of …