Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Ind
 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 

24 Cat-1-groups
 24.1  

24 Cat-1-groups

24.1  

24.1-1 AutomorphismGroupAsCatOneGroup
‣ AutomorphismGroupAsCatOneGroup( G )( function )

Inputs a group G and returns the Cat-1-group C corresponding to the crossed module G→ Aut(G).

Examples: 1 , 2 , 3 , 4 , 5 

24.1-2 HomotopyGroup
‣ 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 

24.1-3 HomotopyModule
‣ 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.

Examples: 1 

24.1-4 QuasiIsomorph
‣ 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.

Examples: 1 , 2 , 3 

24.1-5 ModuleAsCatOneGroup
‣ 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:

24.1-6 MooreComplex
‣ 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:

24.1-7 NormalSubgroupAsCatOneGroup
‣ 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:

24.1-8 XmodToHAP
‣ 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 

 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 
Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Ind

generated by GAPDoc2HTML