author | Scott Morrison <scott@tqft.net> |
Sun, 30 May 2010 11:35:14 -0700 | |
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\documentclass[11pt,leqno]{article} |
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%\usepackage{amsthm} |
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\input{text/article_preamble} |
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\input{text/top_matter} |
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%\title{Blob Homology} |
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\title{The Blob Complex} |
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\begin{document} |
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\makeatletter |
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[revision $\ge$ 276; $\ge$ 30 May 2010] |
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\textbf{Draft version, read with caution.} |
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\medskip |
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\nn{need to remove or at least water down this warning for the arxiv version} |
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\noindent |
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{\bf Warning:} This draft is draftier than you might expect. |
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More specifically, |
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\begin{itemize} |
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\item Some sections are missing. |
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\item Many sections are incomplete. |
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In most cases the incompleteness is noted, but occasionally it isn't. |
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\item Some sections were written nearly two years ago, and are now outdated. |
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\item There are not yet enough citations to similar work of other people. |
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\end{itemize} |
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Despite all this, there's probably enough decipherable material |
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here to interest the motivated reader. |
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On the other hand, if you are only going to read this paper once, |
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{\bf then don't read this version,} as a more complete version will be available in a couple of months. |
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\nn{maybe to do: add appendix on various versions of acyclic models} |
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\paragraph{To do list} |
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\begin{itemize} |
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\item[1] (K) tweak intro |
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\item[2] (S) needs explanation that this will be superseded by the n-cat |
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definitions in \S 7. |
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\item[2] (S) incorporate improvements from later |
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\item[2.3] (S) foreshadow generalising; quotient to resolution |
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\item[3] (K) look over blob homology section again |
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\item[4] (S) basic properties, not much to do |
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\item[5] (K) finish the lemmas in the Hochschild section |
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\item[6] (K) proofs need finishing, then (S) needs to confirm details and try |
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to make more understandable |
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\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? |
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\item[7.6] is new! (S) read |
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\item[8] improve the beginning, (K) small blobs, finish proof for products, |
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check the argument about maps |
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\item[9] (K) proofs trail off |
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\item[10] (S) read what's already here |
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\item[A] may need to weaken statement to get boundaries working (K) finish |
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\item[B] (S) look at this, decide what to keep |
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\item Make clear exactly what counts as a "blob diagram", and search for |
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"blob diagram" |
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\item Say something about stabilizing an $n$-category (centre), taking the top $k$ levels of a category, and the stabilization hypothesis? |
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\end{itemize} |
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\tableofcontents |
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\input{text/intro} |
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\input{text/hochschild} |
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\input{text/ncat} |
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\input{text/deligne} |
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\appendix |
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% ---------------------------------------------------------------- |
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%\newcommand{\urlprefix}{} |
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\bibliographystyle{plain} |
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%Included for winedt: |
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%input "bibliography/bibliography.bib" |
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\bibliography{bibliography/bibliography} |
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% ---------------------------------------------------------------- |
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This paper is available online at \arxiv{?????}, 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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% A GTART necessity: |
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% \Addresses |
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% ---------------------------------------------------------------- |
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\end{document} |
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% ---------------------------------------------------------------- |
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