<Chapter><Heading> Induced equivariant chain maps</Heading> <Section><Heading> </Heading>
<ManSection> <Func Name="EquivariantChainMap" Arg="R,S,f"/> <Description> <P/> Inputs a <M>ZG</M>-resolution <M>R</M>, a <M>ZG'-resolution S, and a group homomorphism f : G \longrightarrow G'</M>. It outputs a component object <M>M</M> with the following components. <P/> <List> <Item> <M>M!.source</M> is the resolution <M>R</M>.</Item> <Item> <M>M!.target</M> is the resolution <M>S</M>.</Item> <Item><M>M!.mapping(w,n)</M> is a function which gives the image in <M>S_n</M>, under a chain map induced by <M>f</M>, of a word <M>w</M> in <M>R_n</M>. (Here <M>R_n</M> and <M>S_n</M> are the <M>n</M>-th modules in the resolutions <M>R</M> and <M>S</M>.)</Item> <Item> <M>F!.properties</M> is a list of pairs such as ["type", "equivariantChainMap"].</Item> </List> <P/> The resolution <M>S</M> must have a contracting homotopy. <P/><B>Examples:</B> <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL> , <URL><Link>../www/SideLinks/About/aboutCohomologyRings.html</Link><LinkText>2</LinkText></URL> , <URL><Link>../www/SideLinks/About/aboutPoincareSeries.html</Link><LinkText>3</LinkText></URL> , <URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>4</LinkText></URL>
</Description> </ManSection> </Section> </Chapter>
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