author | Kevin Walker <kevin@canyon23.net> |
Wed, 22 Sep 2010 19:01:41 -0700 | |
changeset 554 | 62d6db8c2ead |
parent 522 | a60c035e53bd |
child 560 | b138ee4a5938 |
permissions | -rw-r--r-- |
189 | 1 |
\documentclass[11pt,leqno]{amsart} |
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%\usepackage{amsthm} |
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\newcommand{\pathtotrunk}{./} |
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\input{text/article_preamble} |
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\input{text/top_matter} |
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\input{text/kw_macros} |
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%\title{Blob Homology} |
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\title{Sandbox} |
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\begin{document} |
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456
a5d75e0f9229
filtration -> simplex, and another diagram
Scott Morrison <scott@tqft.net>
parents:
443
diff
changeset
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\begin{figure}[t] |
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\begin{center} |
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\begin{tikzpicture} |
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\node(A) at (-4,0) { |
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\begin{tikzpicture}[scale=.8, fill=blue!15!white] |
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\filldraw[line width=1.5pt] (-.4,1) .. controls +(-1,-.1) and +(-1,0) .. (0,-1) |
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.. controls +(1,0) and +(1,-.1) .. (.4,1) -- (.4,3) |
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.. controls +(3,-.4) and +(3,0) .. (0,-3) |
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.. controls +(-3,0) and +(-3,-.1) .. (-.4,3) -- cycle; |
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\node at (0,-2) {$X$}; |
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\node (W) at (-2.7,-2) {$W$}; |
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\node (Y1) at (-1.2,3.5) {$Y$}; |
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\node (Y2) at (1.4,3.5) {$Y$}; |
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\node[outer sep=2.3] (y1e) at (-.4,2) {}; |
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\node[outer sep=2.3] (y2e) at (.4,2) {}; |
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\node (we1) at (-2.2,-1.1) {}; |
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\node (we2) at (-.6,-.7) {}; |
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\draw[->] (Y1) -- (y1e); |
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\draw[->] (Y2) -- (y2e); |
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\draw[->] (W) .. controls +(0,.5) and +(-.5,-.2) .. (we1); |
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\draw[->] (W) .. controls +(.5,0) and +(-.2,-.5) .. (we2); |
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\end{tikzpicture} |
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}; |
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\node(B) at (4,0) { |
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\begin{tikzpicture}[scale=.8, fill=blue!15!white] |
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\fill (0,1) .. controls +(-1,0) and +(-1,0) .. (0,-1) |
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.. controls +(1,0) and +(1,0) .. (0,1) -- (0,3) |
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.. controls +(3,0) and +(3,0) .. (0,-3) |
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.. controls +(-3,0) and +(-3,0) .. (0,3) -- cycle; |
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\draw[line width=1.5pt] (0,1) .. controls +(-1,0) and +(-1,0) .. (0,-1) |
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.. controls +(1,0) and +(1,0) .. (0,1); |
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\draw[line width=1.5pt] (0,3) .. controls +(3,0) and +(3,0) .. (0,-3) |
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.. controls +(-3,0) and +(-3,0) .. (0,3); |
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\draw[line width=.5pt, black!65!white] (0,1) -- (0,3); |
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\node at (0,-2) {$X\sgl$}; |
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\node (W) at (2.7,-2) {$W\sgl$}; |
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\node (we1) at (2.2,-1.1) {}; |
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\node (we2) at (.6,-.7) {}; |
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\draw[->] (W) .. controls +(0,.5) and +(.5,-.2) .. (we1); |
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\draw[->] (W) .. controls +(-.5,0) and +(.2,-.5) .. (we2); |
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\end{tikzpicture} |
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}; |
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\draw[->, red!80!green, line width=2pt] (A) -- node[above, black] {glue} (B); |
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\end{tikzpicture} |
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\end{center} |
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\caption{Gluing with corners} |
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\label{fig:gluing-with-corners} |
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\end{figure} |
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blah |
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\vfill\eject |
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456
a5d75e0f9229
filtration -> simplex, and another diagram
Scott Morrison <scott@tqft.net>
parents:
443
diff
changeset
|
79 |
|
498
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
80 |
\begin{tikzpicture} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\newcommand{\rr}{6} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\newcommand{\vertex}{node[circle,fill=black,inner sep=1pt] {}} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
83 |
|
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
84 |
\node(A) at (0,0) { |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
85 |
\begin{tikzpicture} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\node[red,left] at (0,0) {$y$}; |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\draw (0,0) \vertex arc (-120:-105:\rr) node[red,below] {$a$} arc(-105:-90:\rr) \vertex node[red,below](x2) {$x$}; |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\draw (0,0) \vertex arc (120:105:\rr) node[red,above] {$a$} arc (105:90:\rr) \vertex node[red,above](x1) {$x$} -- (x2); |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
89 |
\begin{scope} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
90 |
\path[clip] (0,0) arc (-120:-60:\rr) arc (60:120:\rr); |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
91 |
\foreach \x in {0,0.24,...,3} { |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
92 |
\draw[green!50!brown] (\x,1) -- (\x,-1); |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\end{scope} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\draw[red, decorate,decoration={brace,amplitude=5pt}] ($(x1)+(0.2,-0.2)$) -- ($(x2)+(0.2,0.2)$) node[midway, xshift=0.7cm] {$x \times I$}; |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\end{tikzpicture} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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}; |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
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|
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\node(B) at (-4,-4) { |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
100 |
\begin{tikzpicture} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
101 |
\node[red,left] at (0,0) {$y$}; |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\draw (0,0) \vertex |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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arc (120:105:\rr) node[red,above] {$a$} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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arc (105:90:\rr) node[red,above] {$x$} \vertex |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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arc (90:75:\rr) node[red,above] {$x \times I$} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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arc (75:60:\rr) \vertex node[red,right] {$x$} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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arc (-60:-90:\rr) node[red,below] {$a$} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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arc (-90:-120:\rr); |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\begin{scope} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\path[clip] (0,0) arc (-120:-60:\rr) arc (60:120:\rr); |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\foreach \x in {0,0.48,...,9} { |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\draw[green!50!brown] (\x/4,1) -- (\x,-1); |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
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} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\end{scope} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\end{tikzpicture} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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}; |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
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|
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\node(C) at (4,-4) { |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\begin{tikzpicture}[y=-1cm] |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\node[red,left] at (0,0) {$y$}; |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\draw (0,0) \vertex |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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arc (120:105:\rr) node[red,below] {$a$} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
123 |
arc (105:90:\rr) node[red,below] {$x$} \vertex |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
124 |
arc (90:75:\rr) node[red,below] {$x \times I$} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
125 |
arc (75:60:\rr) \vertex node[red,right] {$x$} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
126 |
arc (-60:-90:\rr) node[red,above] {$a$} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
127 |
arc (-90:-120:\rr); |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\begin{scope} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\path[clip] (0,0) arc (-120:-60:\rr) arc (60:120:\rr); |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
130 |
\foreach \x in {0,0.48,...,9} { |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
131 |
\draw[green!50!brown] (\x/4,1) -- (\x,-1); |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
132 |
} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
133 |
\end{scope} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
134 |
\end{tikzpicture} |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
135 |
}; |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
136 |
|
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
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\draw[->] (A) -- (B); |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
138 |
\draw[->] (A) -- (C); |
b98790f0282e
diagram for producing weak identities
Scott Morrison <scott@tqft.net>
parents:
456
diff
changeset
|
139 |
\end{tikzpicture} |
189 | 140 |
\end{document} |