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\title{The Blob Complex}

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

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

\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.

\end{abstract}

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\input{text/intro}

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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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\end{document}

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