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\title{The Blob Complex}

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\begin{abstract}
Given an $n$-manifold $M$ and an $n$-category $\cC$, we define a chain complex
(the ``blob complex") $\bc_*(M; \cC)$.
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 \href{http://arxiv.org/abs/1009.5025}{arXiv:1009.5025}.
\end{abstract}


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\appendix

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This paper is available online at \arxiv{1009.5025}, and at
\url{http://tqft.net/blobs},
and at \url{http://canyon23.net/math/}.

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