7 |
7 |
8 %\title{Blob Homology} |
8 %\title{Blob Homology} |
9 \title{Sandbox} |
9 \title{Sandbox} |
10 \begin{document} |
10 \begin{document} |
11 |
11 |
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12 \begin{align*} |
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13 \begin{tikzpicture}[baseline] |
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14 \node[draw] (c) at (0,0) [circle through = {(1,0)}] {$f$}; |
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15 \node (d) at (c.east) [circle through = {(0.25,0)}] {}; |
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16 \foreach \n in {1,2} { |
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17 \node (p\n) at (intersection \n of c and d) {}; |
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18 \fill (p\n) circle (2pt); |
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19 } |
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20 \begin{scope}[decoration={brace,amplitude=10,aspect=0.5}] |
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21 \draw[decorate] (p2.east) -- node[right=2ex] {$a$} (p1.east); |
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22 \end{scope} |
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23 \end{tikzpicture} & = |
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24 \begin{tikzpicture}[baseline] |
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25 \node[draw] (c) at (0,0) [circle through = {(1,0)}] {}; |
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26 \begin{scope} |
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27 \path[clip] (c) circle (1); |
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28 \node[draw,dashed] (d) at (c.east) [circle through = {(0.25,0)}] {}; |
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29 \foreach \n in {1,2} { |
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30 \node (p\n) at (intersection \n of c and d) {}; |
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31 } |
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32 \node[left] at (c) {$f$}; |
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33 \path[clip] (d) circle (0.75); |
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34 \foreach \y in {1,0.86,...,-1} { |
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35 \draw[green!50!brown] (0,\y)--(1,\y); |
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36 } |
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37 \end{scope} |
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38 \draw[->,blue] (1.5,-1) node[below] {$a \times I$} -- (0.75,0); |
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39 \end{tikzpicture} \\ |
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40 \begin{tikzpicture}[baseline] |
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41 \node[draw] (c) at (0,0) [ellipse, minimum height=2cm,minimum width=2.5cm] {}; |
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42 \draw[dashed] (c.north) -- (c.south); |
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43 \node[right=6] at (c) {$g$}; |
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44 \node[left=6] at (c) {$f$}; |
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45 \end{tikzpicture} & = |
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46 \begin{tikzpicture}[baseline] |
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47 \node[draw] (c) at (0,0) [ellipse, minimum height=2cm,minimum width=2.5cm] {}; |
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48 \node[right=9] at (c) {$g$}; |
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49 \node[left=9] at (c) {$f$}; |
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50 \draw[dashed] (c.north) to[out=-115,in=115] (c.south) to[out=65,in=-65] (c.north); |
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51 \begin{scope} |
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52 \path[clip] (c.north) to[out=-115,in=115] (c.south) to[out=65,in=-65] (c.north); |
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53 \foreach \y in {1,0.86,...,-1} { |
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54 \draw[green!50!brown] (-1,\y)--(1,\y); |
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55 } |
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56 \end{scope} |
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57 \draw[->,blue] (.75,-1.25) node[below] {$a \times I$} -- (0,-0.25); |
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58 \end{tikzpicture} \\ |
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59 \begin{tikzpicture}[baseline] |
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60 \node[draw] (c) at (0,0) [ellipse, minimum height=2cm,minimum width=2.5cm] {}; |
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61 \draw[dashed] (c.north) -- (c.south); |
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62 \node[right=18] at (c) {$g$}; |
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63 \node[left=10] at (c) {$f$}; |
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64 \fill (0,0.4) node (p1) {} circle (2pt); |
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65 \fill (0,-0.4) node (p2) {} circle (2pt); |
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66 \begin{scope}[decoration={brace,amplitude=5,aspect=0.5}] |
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67 \draw[decorate] (p1.east) -- node[right=0.5ex] {\scriptsize $a$} (p2.east); |
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68 \end{scope} |
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69 \end{tikzpicture} & = |
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70 \begin{tikzpicture}[baseline] |
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71 \node[draw] (c) at (0,0) [ellipse, minimum height=2cm,minimum width=2.5cm] {}; |
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72 \node[draw,dashed] (d) at (0,0) [circle, minimum height=1cm,minimum width=1cm] {}; |
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73 \draw[dashed] (c.north) -- (d.north) (d.south) -- (c.south); |
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74 \node[right=18] at (c) {$g$}; |
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75 \node[left=18] at (c) {$f$}; |
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76 \clip (0,0) circle (0.5cm); |
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77 \foreach \y in {1,0.86,...,-1} { |
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78 \draw[green!50!brown] (-1,\y)--(1,\y); |
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79 } |
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80 \end{tikzpicture} \\ |
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81 \end{align*} |
12 |
82 |
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83 \begin{tikzpicture} |
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84 \node[circle,fill=black,inner sep=1pt] (A) at (1.73,0) {}; |
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85 \node[circle,fill=black,inner sep=1pt] (B) at (-1.73,0) {}; |
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86 \draw[dashed] (A) -- (B); |
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87 \node[circle,fill=black,inner sep=1pt] (C) at (0,0) {}; |
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88 \node[circle,fill=black,inner sep=1pt] (D) at (0.8,0) {}; |
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89 \begin{scope}[yshift=-1cm] |
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90 \path[clip] (0,0) circle (2); |
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91 \begin{scope}[yshift=2cm] |
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92 \draw (0,0) circle (2); |
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93 \node[circle,fill=black,inner sep=1pt] (L2) at (-90:2) {}; |
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94 \node[circle,fill=black,inner sep=1pt] (L1) at (-120:2) {}; |
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95 \end{scope} |
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96 \end{scope} |
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97 \begin{scope}[yshift=1cm] |
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98 \path[clip] (0,0) circle (2); |
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99 \begin{scope}[yshift=-2cm] |
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100 \draw (0,0) circle (2); |
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101 \node[circle,fill=black,inner sep=1pt] (U) at (90:2) {}; |
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102 \end{scope} |
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103 \end{scope} |
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104 \begin{scope} |
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105 \path[clip] (0,1) circle (2); |
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106 \path[clip] (0,-1) circle (2); |
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107 |
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108 \end{scope} |
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109 \end{tikzpicture} |
13 \end{document} |
110 \end{document} |