Morrison, ScottWalker, Kevin2015-12-071364-0380http://hdl.handle.net/1885/26725Given an n-manifold M and an n-category C, we define a chain complex (the "blob complex") B*(M;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. This is the published version of arXiv:1009.5025.201210.2140/gt.2012.16.14812015-12-07