  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.
