GAP (HAP commands) - Chapter 7: Induced equivariant chain maps

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7 Induced equivariant chain maps
7.1
7.1-1 EquivariantChainMap

### 7 Induced equivariant chain maps

#### 7.1

##### 7.1-1 EquivariantChainMap

`‣ EquivariantChainMap`( R, S, f ) | ( function )

Inputs a \(ZG\)-resolution \(R\), a \(ZG'\)-resolution \(S\), and a group homomorphism \(f : G \longrightarrow G'\). It outputs a component object \(M\) with the following components.

- \(M!.source\) is the resolution \(R\).

- \(M!.target\) is the resolution \(S\).

- \(M!.mapping(w,n)\) is a function which gives the image in \(S_n\), under a chain map induced by \(f\), of a word \(w\) in \(R_n\). (Here \(R_n\) and \(S_n\) are the \(n\)-th modules in the resolutions \(R\) and \(S\).)

- \(F!.properties\) is a list of pairs such as ["type", "equivariantChainMap"].

The resolution \(S\) must have a contracting homotopy.

Examples: 1 , 2 , 3 , 4

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