Paper III: Typed Transfer, Nonlinear Packets, and Obstruction Theory

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round,line join=round]
2 \draw[fill=black!10,draw=black!40,line width=.35pt,] (0.00000,3.65000) rectangle ++(4.00000,0.75000);
3 \node[] at (2.00000,4.02500) {connection data};
4 \draw[fill=black!10,draw=black!40,line width=.35pt,] (4.00000,3.65000) rectangle ++(2.00000,0.75000);
5 \node[] at (5.00000,4.02500) {$\Gamma_{0\leftarrow2}$};
6 \draw[fill=black!10,draw=black!40,line width=.35pt,] (6.00000,3.65000) rectangle ++(1.80000,0.75000);
7 \node[] at (6.90000,4.02500) {$H$};
8 \draw[fill=black!10,draw=black!40,line width=.35pt,] (7.80000,3.65000) rectangle ++(1.80000,0.75000);
9 \node[] at (8.70000,4.02500) {$D^\times$};
10 \draw[fill=black!10,draw=black!40,line width=.35pt,] (9.60000,3.65000) rectangle ++(3.10000,0.75000);
11 \node[] at (11.15000,4.02500) {$\Gamma_{0\leftarrow2}\Gamma_{2\leftarrow0}$};
12 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.00000,2.70000) rectangle ++(4.00000,0.80000);
13 \node[] at (2.00000,3.10000) {self normalization only};
14 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.00000,2.70000) rectangle ++(2.00000,0.80000);
15 \node[] at (5.00000,3.10000) {$\frac{1}{6}$};
16 \draw[fill=black!0,draw=black!40,line width=.35pt,] (6.00000,2.70000) rectangle ++(1.80000,0.80000);
17 \node[] at (6.90000,3.10000) {$1$};
18 \draw[fill=black!0,draw=black!40,line width=.35pt,] (7.80000,2.70000) rectangle ++(1.80000,0.80000);
19 \node[] at (8.70000,3.10000) {$6/5$};
20 \draw[fill=black!0,draw=black!40,line width=.35pt,] (9.60000,2.70000) rectangle ++(3.10000,0.80000);
21 \node[] at (11.15000,3.10000) {$\frac{5}{6}$};
22 \draw[fill=black!0,draw=black!40,line width=.35pt,] (0.00000,1.70000) rectangle ++(4.00000,0.80000);
23 \node[] at (2.00000,2.10000) {reversible};
24 \draw[fill=black!0,draw=black!40,line width=.35pt,] (4.00000,1.70000) rectangle ++(2.00000,0.80000);
25 \node[] at (5.00000,2.10000) {$\frac{1}{5}$};
26 \draw[fill=black!0,draw=black!40,line width=.35pt,] (6.00000,1.70000) rectangle ++(1.80000,0.80000);
27 \node[] at (6.90000,2.10000) {$\frac{6}{5}$};
28 \draw[fill=black!0,draw=black!40,line width=.35pt,] (7.80000,1.70000) rectangle ++(1.80000,0.80000);
29 \node[] at (8.70000,2.10000) {$6/5$};
30 \draw[fill=black!0,draw=black!40,line width=.35pt,] (9.60000,1.70000) rectangle ++(3.10000,0.80000);
31 \node[] at (11.15000,2.10000) {$1$};
32 \node[] at (6.35000,0.50000) {$\Gamma_{1\leftarrow0}=2,\quad\Gamma_{2\leftarrow1}=3,\quad\Gamma_{2\leftarrow0}=5$};
33 \node[] at (6.35000,-0.20000) {The first row has H = identity at this triangle, but fails its cocycle.};
34 \end{tikzpicture}

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