author | Scott Morrison <scott@tqft.net> |
Thu, 20 Sep 2012 14:24:23 +1000 | |
changeset 980 | 53843b0d9ff2 |
parent 978 | a80cc9f9a65b |
permissions | -rw-r--r-- |
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\documentclass[11pt,leqno]{gtart} |
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\newcommand{\pathtotrunk}{./} |
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\input{preamble} |
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\input{text/article_preamble} |
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\input{text/top_matter} |
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\input{text/kw_macros} |
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\title{The Blob Complex} |
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\begin{document} |
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\makeatletter |
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\@addtoreset{equation}{section} |
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\gdef\theequation{\thesection.\arabic{equation}} |
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\makeatother |
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\begin{abstract} |
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Given an $n$-manifold $M$ and an $n$-category $\cC$, we define a chain complex |
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(the ``blob complex") $\bc_*(M; \cC)$. |
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The blob complex can be thought of as a derived category analogue of the Hilbert space of a TQFT, |
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and also as a generalization of Hochschild homology to $n$-categories and $n$-manifolds. |
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It enjoys a number of nice formal properties, including a higher dimensional |
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generalization of Deligne's conjecture about the action of the little disks operad on Hochschild cochains. |
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Along the way, we give a definition of a weak $n$-category with strong duality which |
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is particularly well suited for work with TQFTs. This is the published version of \href{http://arxiv.org/abs/1009.5025}{arXiv:1009.5025}. |
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\end{abstract} |
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\maketitle |
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\hypersetup{ |
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colorlinks, linkcolor={black}, |
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citecolor={dark-blue}, urlcolor={medium-blue} |
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} |
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\tableofcontents |
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colorlinks, linkcolor={dark-red}, |
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citecolor={dark-blue}, urlcolor={medium-blue} |
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} |
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\input{text/intro} |
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\input{text/tqftreview} |
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\input{text/blobdef} |
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\input{text/basic_properties} |
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\input{text/hochschild} |
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\input{text/evmap} |
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\input{text/ncat} |
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\input{text/a_inf_blob} |
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\input{text/deligne} |
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\appendix |
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\input{text/appendixes/moam} |
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\input{text/appendixes/famodiff} |
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\input{text/appendixes/comparing_defs} |
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%\input{text/comm_alg} |
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% ---------------------------------------------------------------- |
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\newcommand{\urlprefix}{} |
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\bibliographystyle{gtart} |
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\bibliography{bibliography/bibliography} |
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This paper is available online at \arxiv{1009.5025}, and at |
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\url{http://tqft.net/blobs}, |
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and at \url{http://canyon23.net/math/}. |
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% ---------------------------------------------------------------- |
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\end{document} |
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% ---------------------------------------------------------------- |
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