19 [revision $\ge$ 527;  $\ge$ 30 August 2010]

    19 %[revision $\ge$ 527;  $\ge$ 30 August 2010]

    20 %

    21 %{\color[rgb]{.9,.5,.2} \large \textbf{Draft version, read with caution.}}

    22 %We're in the midst of revising this, and hope to have a version on the arXiv soon.

    21 {\color[rgb]{.9,.5,.2} \large \textbf{Draft version, read with caution.}}

    24 \begin{abstract}

    22 We're in the midst of revising this, and hope to have a version on the arXiv soon.

    25 Given an $n$-manifold $M$ and an $n$-category $\cC$, we define a chain complex

    26 (the ``blob complex") $\bc_*(M; \cC)$.

    27 The blob complex can be thought of as a derived category version of the Hilbert space of a TQFT, 

    28 or as a generalization of Hochschild homology to $n$-categories and $n$-manifolds.

    29 It enjoys a number of nice formal properties, including a higher dimensional

    30 generalization of Deligne's conjecture about the action of the little disks operad on Hochschild cochains.

    31 Along the way, we give a definition of a weak $n$-category with strong duality which

    32 is particularly well suited for work with TQFTs.

    33 \end{abstract}