‣ AutomorphismGroupAsCatOneGroup( G ) | ( function ) |
Inputs a group G and returns the Cat-1-group C corresponding to the crossed module G→ Aut(G).
‣ HomotopyGroup( C, n ) | ( function ) |
Inputs a cat-1-group C and an integer n. It returns the nth homotopy group of C.
Examples: 1 , 2 , 3 , 4 , 5 , 6 , 7
‣ HomotopyModule( C, 2 ) | ( function ) |
Inputs a cat-1-group C and an integer n=2. It returns the second homotopy group of C as a G-module (i.e. abelian G-outer group) where G is the fundamental group of C.
‣ QuasiIsomorph( C ) | ( function ) |
Inputs a cat-1-group C and returns a cat-1-group D for which there exists some homomorphism C→ D that induces isomorphisms on homotopy groups.
This function was implemented by Le Van Luyen.
‣ ModuleAsCatOneGroup | ( global variable ) |
Inputs a group G, an abelian group M and a homomorphism α: G→ Aut(M). It returns the Cat-1-group C corresponding th the zero crossed module 0: M→ G.
Examples:
‣ MooreComplex( C ) | ( function ) |
Inputs a cat-1-group C and returns its Moore complex as a G-complex (i.e. as a complex of groups considered as 1-outer groups).
Examples:
‣ NormalSubgroupAsCatOneGroup( G, N ) | ( function ) |
Inputs a group G with normal subgroup N. It returns the Cat-1-group C corresponding th the inclusion crossed module N→ G.
Examples:
‣ XmodToHAP( C ) | ( function ) |
Inputs a cat-1-group C obtained from the Xmod package and returns a cat-1-group D for which IsHapCatOneGroup(D) returns true.
It returns "fail" id C has not been produced by the Xmod package.
Examples: 1
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