author | Scott Morrison <scott@tqft.net> |
Sun, 27 Jun 2010 19:04:53 -0700 | |
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parent 398 | 2a9c637182f0 |
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\input{text/article_preamble} |
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\input{text/top_matter} |
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\title{The Blob Complex} |
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[revision $\ge$ 393; $\ge$ 24 June 2010] |
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{\color[rgb]{.9,.5,.2} \large \textbf{Draft version, read with caution.}} |
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We're in the midst of revising this, and hope to have a version on the arXiv soon. |
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\noop{ |
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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\item[2] (S) needs explanation that this will be superseded by the n-cat |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, 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 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}. |
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\nn{KW: Do we need to do this? We don't really classify field theories. |
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I suppose our work could be interpreted as a alternative proof of cobordism hypothesis, but we |
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don't emphasize that at the moment. |
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On the other hand, I'm happy to do Chris a favor by citing this stuff.} |
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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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\item say something about starting with semisimple n-cat (trivial?? not trivial?) |
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\item maybe to do: add appendix on various versions of acyclic models |
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\end{itemize} |
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} % end \noop |
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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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\appendix |
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\input{text/appendixes/famodiff} |
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\input{text/appendixes/smallblobs} |
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% ---------------------------------------------------------------- |
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%\newcommand{\urlprefix}{} |
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\bibliographystyle{plain} |
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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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% ---------------------------------------------------------------- |
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\end{document} |
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