= Betti number
{c}
{title2=$b_k=\dim_{\mathbb R}H_k(M;\mathbb R)$}
{wiki}
A Betti number is the dimension of a real <singular homology> group; on a smooth manifold it is also the dimension of the corresponding <de Rham cohomology> group. For a finite-dimensional cohomology group on a closed Riemannian manifold, it equals the dimension of its space of harmonic representatives. Betti numbers can increase under a finite cover, so equality is a separate hypothesis, not a general covering-space theorem.
Back to article page
