Homology Group/Examples
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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.