In mathematics (especially algebraic topology and abstract algebra), homology (in part from Greek ὁμός homos "identical") 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. Homology groups were originally defined in algebraic topology. However, similar constructions are available in a wide variety of other contexts, such as groups, Lie algebras, Galois theory, and algebraic geometry. The original motivation for defining homology groups was the observation that two shapes can be distinguished...