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Differential group

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An Abelian group $C$ with a given endomorphism $d : C \rightarrow C$ such that $d^2 = 0$. This endomorphism is called a differential. The elements of a differential group are known as chains; the elements of the kernel $\ker d$ are known as cycles; and the elements of the image $\mathrm{im}\, d$ are called boundaries. The homology of $C$ is the quotient $\ker d / \mathrm{im}\,d$.

References

  • [a1] E.H. Spanier, "Algebraic topology", McGraw-Hill (1966) pp. 156
How to Cite This Entry:
Differential group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Differential_group&oldid=53679
This article was adapted from an original article by A.V. Mikhalev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article