<Chapter><Heading> Induced equivariant chain maps</Heading> <Table Align="|l|" > <Row> <Item> <Index> EquivariantChainMap</Index> <C> EquivariantChainMap(R,S,f)</C> <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. </Item> </Row> </Table> </Chapter>