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    Homology

    Basic definition

    Homology is a mathematical concept used in many branches of algebra and topology that involves a topological invariant known as a homology group.

    Detailed definition

    Homology is a concept that is used in many branches of algebra and topology. Historically, the term "homology" was first used in a topological sense by Poincaré. To him, it meant pretty much what is now called a bordism, meaning that a homology was thought of as a relation between manifolds mapped into a manifold. Such manifolds form a homology when they form the boundary of a higher-dimensional manifold inside the manifold in question.

    Educational grade level

    graduate school level

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