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
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
|
DeclareGlobalFunction("CellComplexBoundaryCheck");
InstallGlobalFunction(CellComplexBoundaryCheck,
function(C)
local N,i,j,Elts,pos,CLeftCosetElt,Mult,bdr,w,k, Boundary;
i:=0;
while C!.dimension(i)>0 do
i:=i+1;
od;
N:=i-1;
Elts:=C!.elts;
pos:=function(g)
local posit;
posit:=Position(Elts,g);
if posit=fail then
Add(Elts,g);
return Length(Elts);
else
return posit;
fi;
end;
CLeftCosetElt:=function(i,j,g)
return pos(CanonicalRightCountableCosetElement
(C!.stabilizer(AbsInt(i),j),Elts[g]^-1)^-1);
end;
Mult:=function(L,k,g)
local x,w,t,h,y,vv,LL;
vv:=[];
LL:=ShallowCopy(L);
for x in [1..Length(LL)] do
w:=Elts[g]*Elts[LL[x][2]];
t:=CLeftCosetElt(k,AbsInt(LL[x][1]),pos(w));
Add(vv,[C!.action(k,AbsInt(LL[x][1]),t)*C!.action(k,AbsInt(LL[x][1]),pos(w))*LL[x][1],t]);
od;
return vv;
end;
################################
for i in [2..N+1] do
for j in [1..C!.dimension(i)] do
bdr:=StructuralCopy(C!.boundary(i,j));
w:=[];
Boundary:=[];
for k in bdr do
w:=Mult(C!.boundary(i-1,AbsInt(k[1])),i-2,k[2]);
if k[1]<0 then w:=NegateWord(w);fi;
Append(Boundary,w);
od;
Boundary:=AlgebraicReduction(Boundary);
Print([i,j],Boundary);
if not IsEmpty(Boundary) then return false;fi;
od;
od;
return true;
end);
#####################################################################
DeclareProperty("IsGammaSubgroupInSL3Z",IsHAPRationalSpecialLinearGroup);
InstallGlobalFunction( GammaSubgroupInSL3Z,
function(n)
local groupname, C, G;
groupname:=Concatenation("Gamma_",String(n),"inSL3Z");
C:=ContractibleGcomplex(groupname);
G:=C!.group;
G!.number:=n;
SetName(G,groupname);
SetIsHAPRationalMatrixGroup(G,true);
SetIsHAPRationalSpecialLinearGroup(G,true);
SetIsGammaSubgroupInSL3Z(G,true);
return G;
############################
end);
####################################################################
#####################################################################
######################
InstallMethod( \in,
"for GammaSubgroupInSL3Z",
[ IsMatrix, IsGammaSubgroupInSL3Z ],
function ( g, G )
local groupname, p, n;
groupname:=Name(G);
n:=G!.number;
if n=1 then
if (g[2][1] mod 2 =0)and(g[3][1] mod 2 =0) then
return true;
else return false;
fi;
elif n=2 then
if (g[2][1] mod 2 =0)and(g[3][1] mod 2 =0) and (g[3][2] mod 2 =0)
then return true;
else return false;
fi;
fi;
end );
######################
|
