2 

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     3 \newcommand{\pathtotrunk}{./}

     3 \newcommand{\pathtotrunk}{./}

     4 \input{preamble}

     4 \input{preamble}

     5 \input{text/article_preamble}

     5 \input{text/article_preamble}

     6 \input{text/top_matter}

     6 \input{text/top_matter}

    13 \makeatletter

    13 \makeatletter

    14 \@addtoreset{equation}{section}

    14 \@addtoreset{equation}{section}

    15 \gdef\theequation{\thesection.\arabic{equation}}

    15 \gdef\theequation{\thesection.\arabic{equation}}

    16 \makeatother

    16 \makeatother

    17 

    17 

    20 \begin{abstract}

    18 \begin{abstract}

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

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

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

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

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

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

    24 and also as a generalization of Hochschild homology to $n$-categories and $n$-manifolds.

    22 and also as a generalization of Hochschild homology to $n$-categories and $n$-manifolds.

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

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

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

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

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

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

    28 is particularly well suited for work with TQFTs. This is the published version of \href{http://arxiv.org/abs/1009.5025}{arXiv:1009.5025}.

    26 is particularly well suited for work with TQFTs. This is the published version of \href{http://arxiv.org/abs/1009.5025}{arXiv:1009.5025}.

    29 \end{abstract}

    27 \end{abstract}

    30 

    32 

    31 \hypersetup{

    33 \hypersetup{

    32     colorlinks, linkcolor={black},

    34     colorlinks, linkcolor={black},

    33     citecolor={dark-blue}, urlcolor={medium-blue}

    35     citecolor={dark-blue}, urlcolor={medium-blue}

    34 }

    36 }

    69 \input{text/appendixes/comparing_defs}

    71 \input{text/appendixes/comparing_defs}

    70 

    72 

    71 %\input{text/comm_alg}

    73 %\input{text/comm_alg}

    72 

    74 

    73 % ----------------------------------------------------------------

    75 % ----------------------------------------------------------------

    76 \bibliography{bibliography/bibliography}

    78 \bibliography{bibliography/bibliography}

    77 % ----------------------------------------------------------------

    79 % ----------------------------------------------------------------

    78 

    80 

    79 This paper is available online at \arxiv{1009.5025}, and at

    81 This paper is available online at \arxiv{1009.5025}, and at

    80 \url{http://tqft.net/blobs},

    82 \url{http://tqft.net/blobs},