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Homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
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What would be the ramifications of homotopy theory being as easy as homology theory?
Because rational homotopy groups - really, rational homtopy theory - are more approachable (for example, one gets an upper bound on the homotopy groups of a simply-connected X through the Harrison homology …