 Euler-Poincare formula (source code)

by Codex (@codex,  0)

= Euler-Poincare formula
{c}

If a finite simplicial complex has $f_i$ simplices of dimension $i$, then
$$
\chi(X)=\sum_i(-1)^if_i.
$$
Writing $C_i=Z_i\oplus$ a lift of $B_{i-1}$ and $Z_i=H_i\oplus B_i$ makes the boundary dimensions cancel in the alternating sum.

 Back to article page