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%\title{Blob Homology}

\title{The Blob Complex}

\begin{document}

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\textbf{Draft version, do not distribute.}

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%[19 October 2009, rev. $>$ 129]

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\noindent

{\bf Warning:} This draft is draftier than you might expect.

More specifically,

\begin{itemize}

\item Some sections are missing.

\item Many sections are incomplete.

In some cases the incompleteness is noted, in some cases not.

\item Some sections have been rewritten, but the older, obsolete version of

the section has not been deleted yet.

\item Some sections were written nearly two years ago, and are now outdated.

\item Some sections have not been proof-read.

\item There are not yet enough citations to similar work of other people.

\item Due to multiple authors and multiple, disconnected episodes of writing,

the various parts do not cohere as well as they should. 

\end{itemize}

Despite all this, there's probably enough decipherable material

here to interest the motivated reader.

On the other hand, if you are only going to read this paper once,

{\bf then don't read this version,} as a more complete version will be available in a couple of months.

\tableofcontents

%\noop{

\section*{Old To Do list}

\subsection*{What else?...}

\relax

\nn{should move this to do list elsewhere}

\begin{itemize}

\item higher priority

\begin{itemize}

\item K\&S: learn the state of the art in A-inf categories

(tensor products, Kadeishvili result, ...)

\item section describing intended applications

\item say something about starting with semisimple n-cat (trivial?? not trivial?)

\item need to make up our minds about quasi-isomorphic vs hty equivalent

\end{itemize}

\item medium priority

\begin{itemize}

\item $n=2$ examples

\item dimension $n+1$ (generalized Deligne conjecture?)

\item should be clear about PL vs Diff; probably PL is better

(or maybe not)

\item shuffle product vs gluing product (?)

\item connection between $A_\infty$ operad and topological $A_\infty$ cat defs

\end{itemize}

\item lower priority

\begin{itemize}

\item Derive Hochschild standard results from blob point of view?

\item Kh

\item Mention somewhere \cite{MR1624157} ``Skein homology''; it's not directly related, but has similar motivations.

\end{itemize}

\end{itemize}

%} %end \noop

\input{text/intro}

\input{text/definitions}

\input{text/basic_properties}

\input{text/hochschild}

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\input{text/ncat}

\input{text/a_inf_blob}

\input{text/comm_alg}

\appendix

\input{text/appendixes/famodiff}

\input{text/appendixes/comparing_defs}

\input{text/appendixes/misc_appendices}

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

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

and at \url{http://canyon23.net/math/}.

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