\begin{eqnarray}
2 &=& 1_1 + 1_2 - c( 1_1, 1_2) \\
3 &=& 1_1 + 1_2 + 1_3 - c( 1_1, 1_2) - c( 1_2, 1_3) - c( 1_3, 1_1) + c( 1_1, 1_2, 1_3) \\
&=& 2_{12} + 2_{23} + 2_{31} + c(1_1,1_2,1_3)\\
4 &=& 3_{123} + 3_{234} + 3_{341}+3_{412} - c(1_1,1_2,1_3,1_4)
\end{eqnarray}
Čech cohomology
$f: U_1\cap U_2\cap \cdots\cap U_n \mapsto a\Leftrightarrow f(1,2,...,n)=a$
\begin{eqnarray}
(\delta f)(1, 2) &=& f(1) + f(2) \\
(\delta f)(1,2,3) &=& f(1,2) + f(2,3) + f(3,1) \\
(\delta f)(1,2,3,4) &=& f(1,2,3) + f(2,3,4) + f(3,4,1) + f(4,1,2)
\end{eqnarray}
イメージ的に$c(1_1,1_2,...,1_r)$は$H^r(\mathcal{U}; A)$の元？
