16 \begin{figure}[t]

    17 \begin{center}

    18 \begin{tikzpicture}

    19 

    20 \node(A) at (-4,0) {

    21 \begin{tikzpicture}[scale=.8, fill=blue!15!white]

    22 \filldraw[line width=1.5pt] (-.4,1) .. controls +(-1,-.1) and +(-1,0) .. (0,-1)

    23 		.. controls +(1,0) and +(1,-.1) .. (.4,1) -- (.4,3)

    24 		.. controls +(3,-.4) and +(3,0) .. (0,-3)

    25 		.. controls +(-3,0) and +(-3,-.1) .. (-.4,3) -- cycle;

    26 \node at (0,-2) {$X$};

    27 \node (W) at (-2.7,-2) {$W$};

    28 \node (Y1) at (-1.2,3.5) {$Y$};

    29 \node (Y2) at (1.4,3.5) {$Y$};

    30 \node[outer sep=2.3] (y1e) at (-.4,2) {};

    31 \node[outer sep=2.3] (y2e) at (.4,2) {};

    32 \node (we1) at (-2.2,-1.1) {};

    33 \node (we2) at (-.6,-.7) {};

    34 \draw[->] (Y1) -- (y1e);

    35 \draw[->] (Y2) -- (y2e);

    36 \draw[->] (W) .. controls +(0,.5) and +(-.5,-.2) .. (we1);

    37 \draw[->] (W) .. controls +(.5,0) and +(-.2,-.5) .. (we2);

    38 \end{tikzpicture}

    39 };

    40 

    41 \node(B) at (4,0) {

    42 \begin{tikzpicture}[scale=.8, fill=blue!15!white]

    43 \fill (0,1) .. controls +(-1,0) and +(-1,0) .. (0,-1)

    44 		.. controls +(1,0) and +(1,0) .. (0,1) -- (0,3)

    45 		.. controls +(3,0) and +(3,0) .. (0,-3)

    46 		.. controls +(-3,0) and +(-3,0) .. (0,3) -- cycle;

    47 \draw[line width=1.5pt] (0,1) .. controls +(-1,0) and +(-1,0) .. (0,-1)

    48 		.. controls +(1,0) and +(1,0) .. (0,1);

    49 \draw[line width=1.5pt] (0,3) .. controls +(3,0) and +(3,0) .. (0,-3)

    50 		.. controls +(-3,0) and +(-3,0) .. (0,3);

    51 \draw[line width=.5pt, black!65!white] (0,1) -- (0,3);

    52 \node at (0,-2) {$X\sgl$};

    53 \node (W) at (2.7,-2) {$W\sgl$};

    54 \node (we1) at (2.2,-1.1) {};

    55 \node (we2) at (.6,-.7) {};

    56 \draw[->] (W) .. controls +(0,.5) and +(.5,-.2) .. (we1);

    57 \draw[->] (W) .. controls +(-.5,0) and +(.2,-.5) .. (we2);

    58 \end{tikzpicture}

    59 };

    60 

    61 

    62 \draw[->, red!80!green, line width=2pt] (A) -- node[above, black] {glue} (B);

    63 

    64 \end{tikzpicture}

    65 \end{center}

    66 \caption{Gluing with corners}

    67 \label{fig:gluing-with-corners}

    68 \end{figure}

    69 

    70 

    71 

    72 

    73 

    74 blah

    75 

    76 \vfill\eject

    77 

    78 

    79 

    80 \begin{tikzpicture}

    81 \newcommand{\rr}{6}

    82 \newcommand{\vertex}{node[circle,fill=black,inner sep=1pt] {}}

    83 

    84 \node(A) at (0,0) {

    85 \begin{tikzpicture}

    86 \node[red,left] at (0,0)  {$y$};

    87 \draw (0,0) \vertex arc (-120:-105:\rr) node[red,below] {$a$} arc(-105:-90:\rr) \vertex node[red,below](x2) {$x$};

    88 \draw (0,0) \vertex arc (120:105:\rr) node[red,above] {$a$} arc (105:90:\rr) \vertex node[red,above](x1) {$x$} -- (x2);

    89 \begin{scope}

    90 	\path[clip] (0,0) arc (-120:-60:\rr) arc (60:120:\rr);

    91 	\foreach \x in {0,0.24,...,3} {

    92 		\draw[green!50!brown] (\x,1) -- (\x,-1);

    93 	}

    94 \end{scope}

    95 \draw[red, decorate,decoration={brace,amplitude=5pt}] ($(x1)+(0.2,-0.2)$) -- ($(x2)+(0.2,0.2)$) node[midway, xshift=0.7cm] {$x \times I$};

    96 \end{tikzpicture}

    97 };

    98 

    99 \node(B) at (-4,-4) {

   100 \begin{tikzpicture}

   101 \node[red,left] at (0,0) {$y$};

   102 \draw (0,0) \vertex 

   103 	arc (120:105:\rr) node[red,above] {$a$}

   104 	arc (105:90:\rr) node[red,above] {$x$} \vertex

   105 	arc (90:75:\rr) node[red,above] {$x \times I$}

   106 	arc (75:60:\rr) \vertex node[red,right] {$x$}

   107 	arc (-60:-90:\rr) node[red,below] {$a$}

   108 	arc (-90:-120:\rr);

   109 \begin{scope}

   110 	\path[clip] (0,0) arc (-120:-60:\rr) arc (60:120:\rr);

   111 	\foreach \x in {0,0.48,...,9} {

   112 		\draw[green!50!brown] (\x/4,1) -- (\x,-1);

   113 	}

   114 \end{scope}

   115 \end{tikzpicture}

   116 };

   117 

   118 \node(C) at (4,-4) {

   119 \begin{tikzpicture}[y=-1cm]

   120 \node[red,left] at (0,0) {$y$};

   121 \draw (0,0) \vertex 

   122 	arc (120:105:\rr) node[red,below] {$a$}

   123 	arc (105:90:\rr) node[red,below] {$x$} \vertex

   124 	arc (90:75:\rr) node[red,below] {$x \times I$}

   125 	arc (75:60:\rr) \vertex node[red,right] {$x$}

   126 	arc (-60:-90:\rr) node[red,above] {$a$}

   127 	arc (-90:-120:\rr);

   128 \begin{scope}

   129 	\path[clip] (0,0) arc (-120:-60:\rr) arc (60:120:\rr);

   130 	\foreach \x in {0,0.48,...,9} {

   131 		\draw[green!50!brown] (\x/4,1) -- (\x,-1);

   132 	}

   133 \end{scope}

   134 \end{tikzpicture}

   135 };

   136 

   137 \draw[->] (A) -- (B);

   138 \draw[->] (A) -- (C);

   139 \end{tikzpicture}