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
|
/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2008, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of the *
* License, or (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* General Public License for more details. *
* *
* You should have received a copy of the GNU General Public *
* License along with this program; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
/* end stub */
#include "algebra/nabeliangroup.h"
#include "manifold/nsimplesurfacebundle.h"
#include "triangulation/ntriangulation.h"
namespace regina {
const int NSimpleSurfaceBundle::S2xS1 = 1;
const int NSimpleSurfaceBundle::S2xS1_TWISTED = 2;
const int NSimpleSurfaceBundle::RP2xS1 = 3;
NTriangulation* NSimpleSurfaceBundle::construct() const {
NTriangulation* ans = new NTriangulation();
if (type == S2xS1) {
ans->insertLayeredLensSpace(0, 1);
} else if (type == S2xS1_TWISTED) {
// Taken from section 3.5.1 of Ben Burton's PhD thesis.
NTetrahedron* r = new NTetrahedron();
NTetrahedron* s = new NTetrahedron();
r->joinTo(1, s, NPerm());
r->joinTo(3, s, NPerm());
r->joinTo(2, s, NPerm(3, 2, 0, 1));
s->joinTo(2, r, NPerm(3, 2, 0, 1));
ans->addTetrahedron(r);
ans->addTetrahedron(s);
} else if (type == RP2xS1) {
// Taken from section 3.5.1 of Ben Burton's PhD thesis.
NTetrahedron* r = new NTetrahedron();
NTetrahedron* s = new NTetrahedron();
NTetrahedron* t = new NTetrahedron();
s->joinTo(0, r, NPerm(0, 1, 2, 3));
s->joinTo(3, r, NPerm(3, 0, 1, 2));
s->joinTo(1, t, NPerm(3, 0, 1, 2));
s->joinTo(2, t, NPerm(0, 1, 2, 3));
r->joinTo(1, t, NPerm(2, 3, 0, 1));
r->joinTo(3, t, NPerm(2, 3, 0, 1));
ans->addTetrahedron(r);
ans->addTetrahedron(s);
ans->addTetrahedron(t);
}
return ans;
}
NAbelianGroup* NSimpleSurfaceBundle::getHomologyH1() const {
NAbelianGroup* ans = new NAbelianGroup();
ans->addRank();
if (type == RP2xS1)
ans->addTorsionElement(2);
return ans;
}
std::ostream& NSimpleSurfaceBundle::writeName(std::ostream& out) const {
if (type == S2xS1)
out << "S2 x S1";
else if (type == S2xS1_TWISTED)
out << "S2 x~ S1";
else if (type == RP2xS1)
out << "RP2 x S1";
return out;
}
std::ostream& NSimpleSurfaceBundle::writeTeXName(std::ostream& out) const {
if (type == S2xS1)
out << "S^2 \\times S^1";
else if (type == S2xS1_TWISTED)
out << "S^2 \\twisted S^1";
else if (type == RP2xS1)
out << "\\mathbb{R}P^2 \\times S^1";
return out;
}
} // namespace regina
|
