View source for Differential 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''.  The ''homology'' of $C$ is the quotient $\ker d / \mathrm{im}\,d$.



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====References====
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  E.H. Spanier,   "Algebraic topology" , McGraw-Hill  (1966)  pp. 156</TD></TR>
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