homology
Part of speech: noun
Morphological type: derivation
Topics: algebra
algebraic-topology
anthropology
biology
chemistry
genetics
geometry
human-sciences
mathematics
medicine
natural-sciences
organic-chemistry
physical-sciences
psychology
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topology
Etymology: From Latin homologia, from Ancient Greek ὁμολογία (homología, “agreement, assent”); compare French homologie. By surface analysis, 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.
Inflected forms:
form: homologies
pos: noun
tags: plural
Senses:
gloss: The relationship of being homologous; a homologous relationship.
pos: noun
tags: countable
uncountable
examples: 1863, George Salmon, A Treatise on Conic Sections, Longman, Brown, Green, Longman, and Roberts, 4th Edition, page 61,
Two triangles are said to be homologous, when the intersections of the corresponding sides lie on the same right line called the axis of homology: prove that the lines joining the corresponding vertices meet in a point [called the centre of homology].
1885, Charles Leudesdorf (translator), Luigi Cremona, Elements of Projective Geometry, Oxford University Press (Clarendon Press), page 11,
Two corresponding straight lines therefore always intersect on a fixed straight line, which we may call s; thus the given figures are in homology, O being the centre, and s the axis, of homology.
gloss: The relationship of being homologous; a homologous relationship.
pos: noun
tags: countable
uncountable
examples: If the homology centre lies on the homology axis, the homology is said to be singular or parabolic; otherwise, it is called non-singular or hyperbolic.
gloss: The relationship of being homologous; a homologous relationship.
pos: noun
tags: countable
uncountable
examples: One encounters a similar situation in homology theory. Beside singular homology, which is a homotopy invariant, and Čech homology, which is a shape invariant, there exists strong homology, which is a strong shape invariant. In the special case of metric compacta, this homology was introduced by N.E. Steenrod in 1940 and is often referred to as the Steenrod homology.
Brieskorn homology spheres are a special case of Siefert fibered homology spheres.
gloss: The relationship of being homologous; a homologous relationship.
pos: noun
tags: countable
uncountable
examples: Because of their connection with both homology and cohomology, chain complexes are an important topic of study in homological algebra.
gloss: The relationship of being homologous; a homologous relationship.
pos: noun
tags: countable
uncountable
gloss: The relationship of being homologous; a homologous relationship.
pos: noun
tags: countable
uncountable
gloss: The relationship of being homologous; a homologous relationship.
pos: noun
tags: countable
uncountable
examples: 2000, Julie A. Hawkins, Chapter 2: A survey of primary homology assessment, Robert Scotland, R. Toby Pennington (editors), Homology and Systematics, Taylor & Francis, The Systematics Association, page 22,
The objective of this study is to classify approaches to primary homology assessment, and to quantify the extent to which different approaches are found in the literature by examining variation in the ways characters are defined and coded in a data matrix.
gloss: The relationship of being homologous; a homologous relationship.
pos: noun
tags: countable
uncountable
gloss: The relationship of being homologous; a homologous relationship.
pos: noun
tags: countable
uncountable
gloss: The relationship of being homologous; a homologous relationship.
pos: noun
tags: countable
uncountable
Related words: analogy
homolog
homologue
homologation
homological
homologism
paromologia
homothety
homotopy
Derived words: axis of homology
center of homology
centre of homology
cohomology
Floer homology
homology axis
homology center
homology centre
homology group
homology modeling
homology modelling
homology sphere
hyperbolic homology
hyperhomology
Khovanov homology
microhomology
nonhomology
parabolic homology
semihomology
sequence homology
singular homology
Translations:
lang: Catalan
word: homologia
lang: Finnish
word: samankaltaisuus
lang: Finnish
word: homologia
lang: French
word: homologie
lang: German
word: Homologie
lang: Irish
word: homalógacht
lang: Italian
word: omologia
lang: Portuguese
word: homologia
lang: Romanian
word: omologie
lang: Finnish
word: homologia
lang: German
word: Homologie
lang: Irish
word: homalógacht
lang: Romanian
word: omologie