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%\title{Blob Homology}

\title{The Blob Complex}

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\textbf{Draft version, read with caution.}

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\nn{need to remove or at least water down this warning for the arxiv version}

\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 most cases the incompleteness is noted, but occasionally it isn't.

\item Some sections were written nearly two years ago, and are now outdated.

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

\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.

\nn{maybe to do: add appendix on various versions of acyclic models}

\paragraph{To do list}

\begin{itemize}

\item[1] (K) tweak intro

\item[2] (S) needs explanation that this will be superseded by the n-cat

definitions in \S 7.

\item[2] (S) incorporate improvements from later

\item[2.3] (S) foreshadow generalising; quotient to resolution

\item[3] (K) look over blob homology section again

\item[4] (S) basic properties, not much to do

\item[5] (K) finish the lemmas in the Hochschild section

\item[6] (K) proofs need finishing, then (S) needs to confirm details and try

to make more understandable

\item[7] (S) do some work here -- identity morphisms are still imperfect. Say something about the cobordism and stabilization hypotheses \cite{MR1355899} in this setting? Say something about $E_n$ algebras?

\item[7.6] is new! (S) read

\item[8] improve the beginning, (K) small blobs, finish proof for products,

check the argument about maps

\item[9] (K) proofs trail off

\item[10] (S) read what's already here

\item[A] may need to weaken statement to get boundaries working (K) finish

\item[B] (S) look at this, decide what to keep

\item Make clear exactly what counts as a "blob diagram", and search for

"blob diagram"

\end{itemize}

\tableofcontents

\input{text/intro}

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\input{text/basic_properties}

\input{text/hochschild}

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\input{text/ncat}

\input{text/a_inf_blob}

\input{text/comm_alg}

\input{text/deligne}

\appendix

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\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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