<Chapter><Heading> Induced equivariant chain maps</Heading>

<Section><Heading> &nbsp;</Heading>

<ManSection>

<Func Name="EquivariantChainMap" Arg="R,S,f"/>
<Description>

<P/>
Inputs a <M>ZG</M>-resolution <M>R</M>, a <M>ZG'</M>-resolution <M>S</M>, 
and a group homomorphism <M>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>../www/SideLinks/About/aboutCohomologyRings.html</Link><LinkText>1</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutPoincareSeries.html</Link><LinkText>2</LinkText></URL>&nbsp;,
<URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>3</LinkText></URL>&nbsp; 

</Description>







































































































</ManSection>

</Section>
</Chapter>

