author | Scott Morrison <scott@tqft.net> |
Mon, 24 Jan 2011 21:50:56 -0800 | |
changeset 699 | 948807543edd |
parent 572 | e0f5ec582725 |
child 732 | ce02614d58b7 |
permissions | -rw-r--r-- |
264
e8a5b2e128af
switching from amsplain to article
Scott Morrison <scott@tqft.net>
parents:
258
diff
changeset
|
1 |
\documentclass[11pt,leqno]{article} |
0 | 2 |
|
8 | 3 |
\newcommand{\pathtotrunk}{./} |
570 | 4 |
\input{preamble} |
100
c5a43be00ed4
No new content, just rearranging (and procrastinating)
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
98
diff
changeset
|
5 |
\input{text/article_preamble} |
c5a43be00ed4
No new content, just rearranging (and procrastinating)
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
98
diff
changeset
|
6 |
\input{text/top_matter} |
c5a43be00ed4
No new content, just rearranging (and procrastinating)
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
98
diff
changeset
|
7 |
\input{text/kw_macros} |
0 | 8 |
|
131 | 9 |
\title{The Blob Complex} |
0 | 10 |
|
11 |
\begin{document} |
|
12 |
||
13 |
\makeatletter |
|
14 |
\@addtoreset{equation}{section} |
|
15 |
\gdef\theequation{\thesection.\arabic{equation}} |
|
16 |
\makeatother |
|
17 |
||
18 |
\maketitle |
|
19 |
||
558
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
20 |
%[revision $\ge$ 527; $\ge$ 30 August 2010] |
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
21 |
% |
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
22 |
%{\color[rgb]{.9,.5,.2} \large \textbf{Draft version, read with caution.}} |
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
23 |
%We're in the midst of revising this, and hope to have a version on the arXiv soon. |
155 | 24 |
|
558
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
25 |
\begin{abstract} |
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
26 |
Given an $n$-manifold $M$ and an $n$-category $\cC$, we define a chain complex |
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
27 |
(the ``blob complex") $\bc_*(M; \cC)$. |
564 | 28 |
The blob complex can be thought of as a derived category analogue of the Hilbert space of a TQFT, |
29 |
and also as a generalization of Hochschild homology to $n$-categories and $n$-manifolds. |
|
558
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
30 |
It enjoys a number of nice formal properties, including a higher dimensional |
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
31 |
generalization of Deligne's conjecture about the action of the little disks operad on Hochschild cochains. |
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
32 |
Along the way, we give a definition of a weak $n$-category with strong duality which |
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
33 |
is particularly well suited for work with TQFTs. |
c393d1202724
added abstract; other misc minor stuff
Kevin Walker <kevin@canyon23.net>
parents:
553
diff
changeset
|
34 |
\end{abstract} |
360
92f0dac39ce3
interim version to put on web page
Kevin Walker <kevin@canyon23.net>
parents:
347
diff
changeset
|
35 |
|
560 | 36 |
\hypersetup{ |
37 |
colorlinks, linkcolor={black}, |
|
38 |
citecolor={dark-blue}, urlcolor={medium-blue} |
|
39 |
} |
|
417
d3b05641e7ca
making quotation marks consistently "American style"
Kevin Walker <kevin@canyon23.net>
parents:
414
diff
changeset
|
40 |
|
264
e8a5b2e128af
switching from amsplain to article
Scott Morrison <scott@tqft.net>
parents:
258
diff
changeset
|
41 |
\tableofcontents |
79 | 42 |
|
560 | 43 |
\hypersetup{ |
44 |
colorlinks, linkcolor={dark-red}, |
|
45 |
citecolor={dark-blue}, urlcolor={medium-blue} |
|
46 |
} |
|
47 |
||
48 |
||
511
cd08d1b9d274
no more new pages for sections
Kevin Walker <kevin@canyon23.net>
parents:
496
diff
changeset
|
49 |
%\let\stdsection\section |
cd08d1b9d274
no more new pages for sections
Kevin Walker <kevin@canyon23.net>
parents:
496
diff
changeset
|
50 |
%\renewcommand\section{\newpage\stdsection} |
496
01b044f87bb0
TOC doesn't need its own new page
Scott Morrison <scott@tqft.net>
parents:
492
diff
changeset
|
51 |
|
100
c5a43be00ed4
No new content, just rearranging (and procrastinating)
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
98
diff
changeset
|
52 |
\input{text/intro} |
0 | 53 |
|
215 | 54 |
\input{text/tqftreview} |
55 |
||
56 |
\input{text/blobdef} |
|
0 | 57 |
|
100
c5a43be00ed4
No new content, just rearranging (and procrastinating)
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
98
diff
changeset
|
58 |
\input{text/basic_properties} |
0 | 59 |
|
15
7340ab80db25
rearranging the Hochschild section. Splitting things up into lemmas, and explaining why those lemmas are what we need.
scott@6e1638ff-ae45-0410-89bd-df963105f760
parents:
13
diff
changeset
|
60 |
\input{text/hochschild} |
7
4ef2f77a4652
small to medium sized changes
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
5
diff
changeset
|
61 |
|
70 | 62 |
\input{text/evmap} |
69 | 63 |
|
100
c5a43be00ed4
No new content, just rearranging (and procrastinating)
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
98
diff
changeset
|
64 |
\input{text/ncat} |
47
939a4a5b1d80
increased line width; start to write commutative algebra results
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
45
diff
changeset
|
65 |
|
113 | 66 |
\input{text/a_inf_blob} |
67 |
||
148 | 68 |
\input{text/deligne} |
22
ada83e7228eb
rearranging; stating all the "properties" up front
scott@6e1638ff-ae45-0410-89bd-df963105f760
parents:
21
diff
changeset
|
69 |
|
ada83e7228eb
rearranging; stating all the "properties" up front
scott@6e1638ff-ae45-0410-89bd-df963105f760
parents:
21
diff
changeset
|
70 |
\appendix |
ada83e7228eb
rearranging; stating all the "properties" up front
scott@6e1638ff-ae45-0410-89bd-df963105f760
parents:
21
diff
changeset
|
71 |
|
492
833bd74143a4
put in a stub appendix for MoAM, but I'm going to go do other things next
Scott Morrison <scott@tqft.net>
parents:
481
diff
changeset
|
72 |
\input{text/appendixes/moam} |
833bd74143a4
put in a stub appendix for MoAM, but I'm going to go do other things next
Scott Morrison <scott@tqft.net>
parents:
481
diff
changeset
|
73 |
|
135 | 74 |
\input{text/appendixes/famodiff} |
75 | 75 |
|
524
edf8798ef477
finished 1st draft of new evmap section; commented out older versions
Kevin Walker <kevin@canyon23.net>
parents:
520
diff
changeset
|
76 |
%\input{text/appendixes/smallblobs} |
317
1c898c2d0ebd
finished smallblobs, except for the issue about coupons, and moved it all to an appendix
Scott Morrison <scott@tqft.net>
parents:
315
diff
changeset
|
77 |
|
135 | 78 |
\input{text/appendixes/comparing_defs} |
114 | 79 |
|
553
94cadcb4831f
killing commutative alg appendix
Kevin Walker <kevin@canyon23.net>
parents:
527
diff
changeset
|
80 |
%\input{text/comm_alg} |
325 | 81 |
|
22
ada83e7228eb
rearranging; stating all the "properties" up front
scott@6e1638ff-ae45-0410-89bd-df963105f760
parents:
21
diff
changeset
|
82 |
% ---------------------------------------------------------------- |
23
7b0a43bdd3c4
writing definitions of topological a_\infty categories, modules, etc.
scott@6e1638ff-ae45-0410-89bd-df963105f760
parents:
22
diff
changeset
|
83 |
%\newcommand{\urlprefix}{} |
572
e0f5ec582725
incorporating statements of results in PNAS article
Scott Morrison <scott@tqft.net>
parents:
570
diff
changeset
|
84 |
\bibliographystyle{alpha} |
22
ada83e7228eb
rearranging; stating all the "properties" up front
scott@6e1638ff-ae45-0410-89bd-df963105f760
parents:
21
diff
changeset
|
85 |
\bibliography{bibliography/bibliography} |
ada83e7228eb
rearranging; stating all the "properties" up front
scott@6e1638ff-ae45-0410-89bd-df963105f760
parents:
21
diff
changeset
|
86 |
% ---------------------------------------------------------------- |
7
4ef2f77a4652
small to medium sized changes
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
5
diff
changeset
|
87 |
|
565 | 88 |
This paper is available online at \arxiv{1009.5025}, and at |
47
939a4a5b1d80
increased line width; start to write commutative algebra results
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
45
diff
changeset
|
89 |
\url{http://tqft.net/blobs}, |
939a4a5b1d80
increased line width; start to write commutative algebra results
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
45
diff
changeset
|
90 |
and at \url{http://canyon23.net/math/}. |
7
4ef2f77a4652
small to medium sized changes
kevin@6e1638ff-ae45-0410-89bd-df963105f760
parents:
5
diff
changeset
|
91 |
|
22
ada83e7228eb
rearranging; stating all the "properties" up front
scott@6e1638ff-ae45-0410-89bd-df963105f760
parents:
21
diff
changeset
|
92 |
% ---------------------------------------------------------------- |
ada83e7228eb
rearranging; stating all the "properties" up front
scott@6e1638ff-ae45-0410-89bd-df963105f760
parents:
21
diff
changeset
|
93 |
\end{document} |
ada83e7228eb
rearranging; stating all the "properties" up front
scott@6e1638ff-ae45-0410-89bd-df963105f760
parents:
21
diff
changeset
|
94 |
% ---------------------------------------------------------------- |
0 | 95 |