Blob homology

Given an n-manifold M and an n-category C , we define a chain complex (the "blob complex") B .M I C/. The blob complex can be thought of as a derived category analogue of the Hilbert space of a TQFT, and also as a generalization of Hochschild homology to n-categories and n-manifolds. It enjoys a number of nice formal properties, including a higher dimensional generalization of Deligne's conjecture about the action of the little disks operad on Hochschild cochains. Along the way, we give a definition of a weak n-category with strong duality which is particularly well suited for work with TQFTs.