|
Let $K$ be an oriented geometric complex of dimension $n$, and for $p = 0, 1, \ldots , n$ let $\alpha_{n}$ be the number of $p$-simplexes of $K$. Then $$\sum_{p = 0}^n (-1)^p \alpha_{p} = \sum_{p=0}^n (-1)^p R_p(K)$$ where $R_{p}(K)$ is the $p$-th Betti number of $K$.
|
Let $K$ be an oriented geometric complex of dimension $n$, and for $p = 0, 1, \ldots n$ let $\alpha_{n}$ be the number of $p$-simplexes of $K$. Then $$\sum_{p = 0}^n (-1)^p \alpha_{p} = \sum_{p=0}^n (-1)^p R_p(K)$$ where $R_{p}(K)$ is the $p$-th Betti number of $K$.
|
