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42 lines
1.7 KiB
TeX
42 lines
1.7 KiB
TeX
% The following answers were used to create this image:
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% - http://tex.stackexchange.com/a/45824/5645 - Grid
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% - http://tex.stackexchange.com/a/373/5645 - Torus
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\begin{tikzpicture}
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\tikzstyle{point}=[circle,thick,draw=black,fill=black,inner sep=0pt,minimum width=4pt,minimum height=4pt]
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\newcommand*{\xMin}{0}%
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\newcommand*{\xMax}{6}%
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\newcommand*{\yMin}{0}%
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\newcommand*{\yMax}{6}%
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\draw (-3.5,0) .. controls (-3.5,2) and (-1.5,2.5) .. (0,2.5);
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\draw[xscale=-1] (-3.5,0) .. controls (-3.5,2) and (-1.5,2.5) .. (0,2.5);
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\draw[rotate=180] (-3.5,0) .. controls (-3.5,2) and (-1.5,2.5) .. (0,2.5);
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\draw[yscale=-1] (-3.5,0) .. controls (-3.5,2) and (-1.5,2.5) .. (0,2.5);
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\draw (-2,.2) .. controls (-1.5,-0.3) and (-1,-0.5) .. (0,-.5) .. controls (1,-0.5) and (1.5,-0.3) .. (2,0.2);
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\draw (-1.75,0) .. controls (-1.5,0.3) and (-1,0.5) .. (0,.5) .. controls (1,0.5) and (1.5,0.3) .. (1.75,0);
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\begin{scope}[shift={(5,-3)}]
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\foreach \i in {\xMin,...,\xMax} {
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\draw [very thin,gray] (\i,\yMin) -- (\i,\yMax) node [below] at (\i,\yMin) {$\i$};
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}
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\foreach \i in {\yMin,...,\yMax} {
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\draw [very thin,gray] (\xMin,\i) -- (\xMax,\i) node [left] at (\xMin,\i) {$\i$};
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}
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\node (P)[point,red] at (1.2,2.2) {};
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\node (Q)[point,red] at (1.2,1.6) {};
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\draw[ultra thick, red] (P) -- (Q);
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\begin{scope}[shift={(2,1)}]
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\node (P)[point,red] at (1.2,2.2) {};
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\node (Q)[point,red] at (1.2,1.6) {};
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\draw[ultra thick, red] (P) -- (Q);
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\end{scope}
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\draw (-1, -0.5) node[below] {$T \xrightarrow{\text{Liften}} \mathbb{R}^2 / \mathbb{Z}^2$};
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\draw[red,dashed] (-5,1.5) ellipse (0.5cm and 1cm);
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\draw[red] (-5,2.5) arc (-270:-90:0.5 and 1) ;
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\end{scope}
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\end{tikzpicture}
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