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\title{The Blob Complex}

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[revision $\ge$ 393;  $\ge$ 24 June 2010]

{\color[rgb]{.9,.5,.2} \large \textbf{Draft version, read with caution.}}
We're in the midst of revising this, and hope to have a version on the arXiv soon.

\noop{

\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\item[2] (S) needs explanation that this will be superseded by the n-cat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, 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 Work in the references Chris Douglas gave us on the classification of local field theories, \cite{BDH-seminar,DSP-seminar,schommer-pries-thesis,0905.0465}.
\nn{KW: Do we need to do this?  We don't really classify field theories.
I suppose our work could be interpreted as a alternative proof of cobordism hypothesis, but we 
don't emphasize that at the moment.  
On the other hand, I'm happy to do Chris a favor by citing this stuff.}

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

\item Say something about stabilizing an $n$-category (centre), taking the top $k$ levels of a category, and the stabilization hypothesis?

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

\item maybe to do: add appendix on various versions of acyclic models


\end{itemize}

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\tableofcontents


\input{text/intro}

\input{text/tqftreview}

\input{text/blobdef}

\input{text/basic_properties}

\input{text/hochschild}

\input{text/evmap}

\input{text/ncat}

\input{text/a_inf_blob}

\input{text/deligne}

\appendix

\input{text/appendixes/famodiff}

\input{text/appendixes/smallblobs}

\input{text/appendixes/comparing_defs}

\input{text/comm_alg}

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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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