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22 %We're in the midst of revising this, and hope to have a version on the arXiv soon. |
22 %We're in the midst of revising this, and hope to have a version on the arXiv soon. |
23 |
23 |
24 \begin{abstract} |
24 \begin{abstract} |
25 Given an $n$-manifold $M$ and an $n$-category $\cC$, we define a chain complex |
25 Given an $n$-manifold $M$ and an $n$-category $\cC$, we define a chain complex |
26 (the ``blob complex") $\bc_*(M; \cC)$. |
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, |
27 The blob complex can be thought of as a derived category analogue of the Hilbert space of a TQFT, |
28 or as a generalization of Hochschild homology to $n$-categories and $n$-manifolds. |
28 and also 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 |
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. |
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 |
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. |
32 is particularly well suited for work with TQFTs. |
33 \end{abstract} |
33 \end{abstract} |
82 %\newcommand{\urlprefix}{} |
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83 \bibliographystyle{plain} |
83 \bibliographystyle{plain} |
84 \bibliography{bibliography/bibliography} |
84 \bibliography{bibliography/bibliography} |
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86 |
86 |
87 This paper is available online at \arxiv{1009.5025}, and at |
87 This paper is available online at \arxiv{?????}, and at |
88 \url{http://tqft.net/blobs}, |
88 \url{http://tqft.net/blobs}, |
89 and at \url{http://canyon23.net/math/}. |
89 and at \url{http://canyon23.net/math/}. |
90 |
90 |
91 % ---------------------------------------------------------------- |
91 % ---------------------------------------------------------------- |
92 \end{document} |
92 \end{document} |