homology group

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homology group [hə′mäl·ə·jē ‚grüp]

(mathematics)

Associated to a topological spaceX,one of a sequence of Abelian groupsH_n(X) that reflect hown-dimensional simplicial complexes can be used to fill upXand also help determine the presence ofn-dimensional holes appearing inX. Also known as Betti group.

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acyclic
Betti group

cohomology group
connectivity number

duality theorem
homological algebra

homology theory
torsion group

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homology
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