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- Homology_(mathematics) abstract "In mathematics (especially algebraic topology and abstract algebra), homology (in part from Greek ὁμός homos "identical") is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a topological space or a group. See singular homology for a concrete version for topological spaces, or group cohomology for a concrete version for groups. For a topological space, the homology groups are generally much easier to compute than the homotopy groups, and consequently one usually will have an easier time working with homology to aid in the classification of spaces.The original motivation for defining homology groups is the observation that shapes are distinguished by their holes. But because a hole is "not there", it is not immediately obvious how to define a hole, or how to distinguish between different kinds of holes. Homology is a rigorous mathematical method for defining and categorizing holes in a shape. As it turns out, subtle kinds of holes exist that homology cannot "see" — in which case homotopy groups may be what is needed.".
- Homology_(mathematics) thumbnail Circle_-_black_simple.svg?width=300.
- Homology_(mathematics) wikiPageExternalLink chomp.rutgers.edu.
- Homology_(mathematics) wikiPageExternalLink linalg.org.
- Homology_(mathematics) wikiPageExternalLink redhom.ii.uj.edu.pl.
- Homology_(mathematics) wikiPageExternalLink 1361982.
- Homology_(mathematics) wikiPageExternalLink 529171.
- Homology_(mathematics) wikiPageExternalLink Kenzo.
- Homology_(mathematics) wikiPageExternalLink Homology_group.
- Homology_(mathematics) wikiPageExternalLink www.gap-system.org.
- Homology_(mathematics) wikiPageExternalLink www.maplesoft.com.
- Homology_(mathematics) wikiPageExternalLink ATchapters.html.
- Homology_(mathematics) wikiPageExternalLink survey.pdf.
- Homology_(mathematics) wikiPageExternalLink perseus.
- Homology_(mathematics) wikiPageID "142432".
- Homology_(mathematics) wikiPageRevisionID "605033737".
- Homology_(mathematics) hasPhotoCollection Homology_(mathematics).
- Homology_(mathematics) id "3720".
- Homology_(mathematics) title "Homology".
- Homology_(mathematics) subject Category:Homology_theory.
- Homology_(mathematics) comment "In mathematics (especially algebraic topology and abstract algebra), homology (in part from Greek ὁμός homos "identical") is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a topological space or a group. See singular homology for a concrete version for topological spaces, or group cohomology for a concrete version for groups.".
- Homology_(mathematics) label "Homologia (matemática)".
- Homology_(mathematics) label "Homologie (Mathematik)".
- Homology_(mathematics) label "Homologie (wiskunde)".
- Homology_(mathematics) label "Homology (mathematics)".
- Homology_(mathematics) label "Homología (matemática)".
- Homology_(mathematics) label "Omologia (topologia)".
- Homology_(mathematics) label "Гомология (математика)".
- Homology_(mathematics) label "تماثل (رياضيات)".
- Homology_(mathematics) label "ホモロジー (数学)".
- Homology_(mathematics) label "同调".
- Homology_(mathematics) sameAs Homologie_(matematika).
- Homology_(mathematics) sameAs Homologie_(Mathematik).
- Homology_(mathematics) sameAs Homología_(matemática).
- Homology_(mathematics) sameAs Omologia_(topologia).
- Homology_(mathematics) sameAs ホモロジー_(数学).
- Homology_(mathematics) sameAs 호몰로지.
- Homology_(mathematics) sameAs Homologie_(wiskunde).
- Homology_(mathematics) sameAs Homologia_(matemática).
- Homology_(mathematics) sameAs m.011yjk.
- Homology_(mathematics) sameAs Q1144780.
- Homology_(mathematics) sameAs Q1144780.
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- Homology_(mathematics) depiction Circle_-_black_simple.svg.
- Homology_(mathematics) isPrimaryTopicOf Homology_(mathematics).