  We summarize our axioms for higher categories, and describe the blob complex.
Fixing an n-category C, the blob complex associates a chain complex B_*(W;C)$
to any n-manifold W. The 0-th homology of this chain complex recovers the usual
topological quantum field theory invariants of W. The higher homology groups
should be viewed as generalizations of Hochschild homology (indeed, when W=S^1
they coincide). The blob complex has a very natural definition in terms of
homotopy colimits along decompositions of the manifold W. We outline the
important properties of the blob complex, and sketch the proof of a
generalization of Deligne's conjecture on Hochschild cohomology and the little
discs operad to higher dimensions.
