Difference between revisions of "Differential group"
From Encyclopedia of Mathematics
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| − | An Abelian group | + | 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''. |
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| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) pp. 156</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) pp. 156</TD></TR> | ||
| + | </table> | ||
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| + | {{TEX|done}} | ||
Revision as of 20:47, 4 December 2016
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.
Comments
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=13399
Differential group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Differential_group&oldid=13399
This article was adapted from an original article by A.V. Mikhalev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article