09_holonomy.tex

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09_holonomy.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm]
2 \node[box,circle] (o) at (-3.6,2.3) {$o$};
3 \node[box,circle] (i) at (-5.5,-.7) {$i$};\node[box,circle] (j) at (-1.7,-.7) {$j$};
4 \draw[arr] (i)--node[lab,left] {$T_i$}(o);\draw[arr] (j)--node[lab,right] {$T_j$}(o);
5 \draw[arr,draw=KomorebiOchre] (j)--node[lab,below] {$\tau_{ij}$}(i);
6 \draw[arr,dashed] (o) to[loop above,min distance=12mm] node[lab,above] {$K_{ij}=T_i\tau_{ij}T_j^{-1}$}(o);
7 \node[lab,text width=5.5cm] at (-3.6,-2) {Exact families correspond to\\fixed anchor vectors.};
8 \begin{scope}[shift={(3.2,.4)}]
9  \draw[thinarr](-2.1,0)--(2.6,0) node[right,lab] {$z_1$};
10  \draw[thinarr](0,-2)--(0,2.3) node[above,lab] {$z_2$};
11  \draw[KomorebiPine,line width=2pt](-2,0)--(2.3,0);
12  \node[dot] (p) at (1.4,1.4) {};\node[dot] (r) at (1.4,-1.4) {};
13  \draw[arr,dashed](p)--(r);
14  \node[lab,anchor=east] at (-.35,1.2) {$H=\operatorname{diag}(1,-1)$};
15  \node[lab,left] at (p) {$(u,v)$};\node[lab,left] at (r) {$(u,-v)$};
16  \node[lab] at (0,-2.6) {$K=\{(u,0):u\in\R\}$};
17 \end{scope}
18 \end{tikzpicture}

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