Reduced homology is a variation of the standard homology theory that is designed to simplify the computation of homology groups, particularly for spaces that are not simply connected. It modifies the chain complex used in homology by reducing the contribution of the 0-th homology group, which captures connected components, thus focusing on higher-dimensional features. This concept plays a crucial role in both simplicial and cellular homology, as it helps provide more streamlined results when dealing with spaces where the number of connected components is not of primary interest.
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