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Definition homology
Etymology
From homo- + -logy.
In topology, first used by French polymath Henri Poincaré, in the sense (close to what is now called a bordism) of a relation between manifolds mapped into a reference manifold: that is, the property of such manifolds that they form the boundary of a higher-dimensional manifold inside the reference manifold. Poincaré's version was eventually replaced by the more general singular homology, which is what mathematicians now mean by homology.
Noun
homology (countable and uncountable, plural homologies)
- A homologous relationship.
- (topology) A theory associating a system of groups to each topological space.
- (algebra) A certain system of groups associated to a chain complex.
- (chemistry) The relationship between the elements in the same group of the periodic table, or between organic compounds in a homologous series.
- (evolutionary theory) A correspondence of structures in two life forms with a common evolutionary origin, such as flippers and hands.
- (genetics) The presence of the same series of bases in related genes.
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