tags: - colorclass/differential geometry ---The Betti numbers are a series of integers that represent the maximal number of cuts that can be made without dividing a space into two separate pieces, or more formally, the rank of the homology groups of a space. They give a measure of the space’s connectivity, with the first Betti number corresponding to the number of loops, the second to the number of voids, and so on. The sum of Betti numbers, under certain conditions, contributes to the Euler Characteristic.