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 ⟶ 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

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