Homology Group/Examples

Examples of Homology Groups

Finite Graph

Let $\Gamma$ denote a finite graph.

The number of independent generators for the group $\map {H_1} \Gamma$ equals the number of independent cycles in $\Gamma$.

Space with Holes

Let $X$ denote a space in $3$ dimensions with $28$ disjoint open balls removed.

Then $\map {H_2} X$ has $28$ independent generators.