<Verb>ChainMap(X,A,Y,B):: PureCubicalComplex, PureCubicalComplex, PureCubicalComplex, PureCubicalComplex --> ChainMap</Verb>
<Verb>ChainMap(f):: RegCWMap --> ChainMap</Verb>
<Verb>ChainMap(f):: SimplicialMap --> ChainComplex</Verb><P/>

<P/>Inputs a pure cubical complex <M>Y</M> and pure cubical sucomplexes
<M>X\subset Y</M>, <M>B\subset Y</M>,<M>A\subset B</M>. It returns the 
induced chain map
<M>f_\ast\colon C_\ast(X/A) \rightarrow C_\ast(Y/B)</M> of cellular chain complexes of pairs. (Typlically one takes <M>A</M> and <M>B</M> to be empty or contractible subspaces, in which case <M>C_\ast(X/A) \simeq C_\ast(X)</M>, <M>C_\ast(Y/B) \simeq C_\ast(Y)</M>.)


<P/> Inputs a map <M>f\colon X \rightarrow Y</M> between two regular 
CW-complexes <M>X,Y</M>   and returns an induced chain map 
<M>f_\ast\colon C_\ast(X) \rightarrow C_\ast(Y)</M> where
 <M>C_\ast(X)</M>, <M>C_\ast(Y)</M> are chain homotopic to (but usually smaller than) the cellular chain complexes of <M>X</M>, <M>Y</M>. 

<P/> Inputs a map <M>f\colon X \rightarrow Y</M> between two simplicial  
complexes <M>X,Y</M>   and returns the induced chain map 
<M>f_\ast\colon C_\ast(X) \rightarrow C_\ast(Y)</M> of cellular chain complexes.

 



