Computing homology refers to the process of determining the homology groups of a topological space, which capture essential features such as holes and connected components. This concept is vital in algebraic topology as it provides algebraic invariants that classify spaces up to homotopy equivalence. Homology is computed using various tools and techniques, with the Mayer-Vietoris sequence being one of the key methods that simplifies calculations for spaces that can be decomposed into simpler parts.
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