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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.

Related terms

dimension axiom | Eilenberg-Steenrod axioms | gadget | geometric homology | graded module | homological algebra | homology boundary | homology class | homology group | homology intersection | simplicial complex | simplicial homology | singular homology

Educational grade level

graduate school level

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