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\title{The Blob Complex}

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%[revision $\ge$ 527;  $\ge$ 30 August 2010]
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%{\color[rgb]{.9,.5,.2} \large \textbf{Draft version, read with caution.}}
%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}

\input{text/tqftreview}

\input{text/blobdef}

\input{text/basic_properties}

\input{text/hochschild}

\input{text/evmap}

\input{text/ncat}

\input{text/a_inf_blob}

\input{text/deligne}

\appendix

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%\input{text/appendixes/smallblobs}

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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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