homology
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English[edit]
Etymology[edit]
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 higherdimensional 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.^{[1]}
Noun[edit]
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.
Usage notes[edit]
 Like many terms that start with a nonsilent h but have emphasis on their second syllable, some people precede homology with an, others with a.
 (evolutionary theory):
 For a discussion of the use of the term homology (and homologous) in biology, see: Patterson, Colin. "Homology in Classical and Molecular Biology." Molecular Biology and Evolution 5, no. 6 (November 1988): 603–625. http://mbe.oxfordjournals.org/cgi/reprint/5/6/603.pdf (accessed 18 December 2009; archived 18 December 2009, http://www.webcitation.org/5m7rn4rCe )
 (topology):
 When used attributively with the name of a topological space (such as in the terms homology nsphere and homology manifold) the reference is to a space whose homology is the same as that of the named space: thus, for example, a homology manifold is a space whose homology is that of some manifold.
 Sometimes used to mean homology group: thus, X did Y by computing the homology of Z means X did Y by computing the homology groups of Z.^{[1]}
 More loosely, the term homology in a space refers to a singular homology group (group of singular homologies).^{[1]}
Derived terms[edit]
Related terms[edit]
Translations[edit]
homologous relationship

biology: correspondence of structures in two life forms with a common evolutionary origin

chemistry: relationship between the elements in the same group of the periodic table
mathematics: theory associating a system of quotient groups to each topological space
mathematics: system of quotient groups associated to a topological space
 The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers. Numbers do not necessarily match those in definitions. See instructions at Wiktionary:Entry layout § Translations.
Translations to be checked
See also[edit]
 Eilenberg–Steenrod axioms on Wikipedia.Wikipedia
 Singular homology on Wikipedia.Wikipedia
References[edit]
 ↑ ^{1.0} ^{1.1} ^{1.2} Homology on Wolfram MathWorld