From manifolds to invariants of E_n-algebras

This thesis represents the first step in an investigation of an interesting class of manifold-theoretic invariants of $E_n$-algebras which generalize topological Hochschild homology. The main goal of this thesis is to give a definition of the invariants, and analyse their geometric framework. These invariants have appeared in the work of Paolo Salvatore and Jacob Lurie (who calls them topological chiral homology), where they are involved in a sort of non-abelian Poincar\'e duality.