Computing homology groups involves determining the algebraic structures that describe topological spaces in terms of their cycles and boundaries. This process provides a way to classify spaces based on their shape and connectivity by assigning a sequence of abelian groups, known as homology groups, to each space. The Mayer-Vietoris sequence is a powerful tool in this context, allowing for the computation of homology groups by breaking a space into simpler pieces and analyzing how these pieces interact.
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