homology

Meaning

Noun

  • The relationship of being homologous; a homologous relationship;
    specifically, such relationship in the context of the geometry of perspective.
  • An automorphism of the projective plane (representing a perspective projection) that leaves all the points of some straight line (the homology axis) fixed and maps all the lines through some single point (the homology centre) onto themselves.
  • A general way of associating a sequence of algebraic objects, such as abelian groups or modules, to a sequence of topological spaces; also used attributively: see Usage notes below.
  • Given a chain complex {Gn} and its associated set of homomorphisms {Hn}, the rule which explains how each Hn maps Gn into the kernel of Gn+1.
  • The relationship, between elements, of being in the same group of the periodic table.
  • The relationship, between organic compounds, of being in the same homologous series.
  • The relationship, between characteristics or behaviours, of having a shared evolutionary or developmental origin;
    specifically, a correspondence between structures in separate life forms having a common evolutionary origin, such as that between flippers and hands.
  • The presence of the same series of bases in different but related genes.
  • The relationship, between temporally separated human beliefs, practices or artefacts, of possessing shared characteristics attributed to genetic or historical links to a common ancestor.

Origin

  • From homo- + -logy.
  • In topology, first used by French polymath Henri PoincarĂ©, 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. PoincarĂ©'s version was eventually replaced by the more general singular homology, which is what mathematicians now mean by homology.

Modern English dictionary

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