Lins S. - Gems, computers, and attractors for 3-manifolds :: Электронная библиотека попечительского совета мехмата МГУ

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Московского государственного университета

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Lins S. - Gems, computers, and attractors for 3-manifolds

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Название: Gems, computers, and attractors for 3-manifolds

Автор: Lins S.

Аннотация:

This text provides a guide to dealing with 3-manifolds by computers. Its emphasis is on presenting algorithms which are used for solving (in practice) the homeomorphism problem for the smallest of these objects. The key concept is the 3-gem, a special kind of edge-colored graph, which encodes the manifold via a ball complex. Passages between 3-gems and more standard presentations like Heegaard diagrams and surgery descriptions are provided. A catalogue of all closed orientable 3-manifolds induced by 3-gems up to 30 vertices is included. In order to help the classification, various invariants are presented, including the new quantum invariants.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 468

Добавлена в каталог: 07.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$e_{1} \equiv e_{2}$       100
$e_{1} \equiv_{j}e_{2}$       100
$G^{fus}_{p,q}$       100
$G^{p}_{1} \# ^{q}G_{2}$       102
$G^{swt}_{a,b}$       11
$G^{\bullet}_{1} \# ^{\bullet}G_{2}$       102
$G^{\bullet}_{1} \# ^{\circ}G_{2}$       102
$G_{1} \# G_{2}$       104
$L_{p,q}$       31
$P^{2}$       104
$p^{2}_{n}$       104
$r^{n}_{i}$       6
$s^{1} \tilde{\times} s^{2}$       117
$s^{1} \times s^{1} \times s^{1}$       30
$s^{1} \times s^{2}$       117
$S^{1} \times S^{2}$ -normalization      263
$S^{2}$       104
$s^{3}$       128
$S^{3}$ -normalization      263
$TS_{1}$ -move      11
$TS_{2}$ -move      11
$TS_{3}$ -move      11
$TS_{4}$ -move      12
$TS_{5}$ -move      12
$TS_{6}$ -move      13
$TS_{p}$ -class      189
$t^{2}$       104
$t^{2}_{n}$       104
$u^{0}$ -forest of rigid 3-gems      182
$u^{0}$ -move      14 154
$u^{0}$ -representative of a 3-gem      142
$u^{0}_{*}$ -move      14 154
$u^{1}$ -move      14 154
$u^{1}_{*}$ -move      14 154
$U^{i}_{m}$ -move on G      145
$u^{i}_{n}$ -attractor, an      89
$u^{i}_{n}$ -attractor, the      89
$u^{i}_{\downarrow}$ -move      145
$u^{n}$ -class      15
$u^{n}$ -classification      15
$u^{n}$ -essential, 3-gem      15
$u^{n}$ -move      14 154
$u^{n}$ -reducible, 3-gem      15
$u^{n}_{*}$ -move      14 154
$v_{1} \equiv_{ij}v_{2}$       100
$\ell_{p,q}$       31
$\hat{k}$ -residue      26
$\lambda(x,y^{*})$       243 244
$\lambda(\Gamma^{TS}_{H})$       141
$\mathcal{S}(b, \ell, t, c)$       33
$\rho$ -move      11 127
$\rho$ -pair      10 40
$\sigma$ -gem      5 53
$\sigma$ -symmetries      54
$\xi$ , the sum of the connectivities of surfaces      65
(n + 1)-graph      1
1-dipole      3 35
1-dipole creation      98
1-dipole in 2-gem      98
1-dipole moves      99
2-dipole      3 37
2-gem      19
3-crystallization      35
3-gem      2 20
A-move, $A^{i}_{r}$ -move      131
Admisible triple      261
Alternating presentation of a group      74
Attractor for a 2-manifold      104
Attractor for a 3-manifold      4
B-move, $B^{i}_{r}$ -move      131
Baloon      39
Baloon move      39
Betti number of a 3-manifold      250
Bigon      2 16
Bipartiteness character of a graph      105
Blackboard framed link      81
Blink      8 81
Blink getting absorbed      85
Bond space of a digraph      106
Breaking of a duet      175
Breaking of a handle      122
Breaking of a trio      107
C-move, $C^{i}_{r}$ -move      132
Cancellation of 1-dipole      35 98
Cancellation of 2-dipole      38
Canonical presentation of a 3-gem      63
Code of a 3-gem      30
Code of bipartite connected (n + 1)-graph      63
Code of bipartite non-connected (n + 1)-graph      64
Code of non-bipartite 3-gem      64
Code-colored edges of a 3-gem      127
Code-numbered vertices of a 3-gem      127
Color specification of a 3-page      130
Color specification of a ladder      130
Color specification of a quasi-cluster      130
Color specification of a quasi-cube      129
Color specification of a TS-configuration      129
Colored triangulation      38
Complementary handlebody      9
Complexity of a 3-gem      178
Complexity of a closed 3-manifold      178
Connected sum along p, q      102 114
Connectivity of a closed surface      65

Contribution of a vertex      137
Creation of 1-dipole      35 98
Creation of 2-dipole      38
Crystallization      35
Cycle space of a digraph      106
D-move, $D^{ij}_{r}$ -move      132
Depth-first search (DFS) exploration of a graph      60
Derived 3-gem      235 236
Digraph      106
Dual construction      3
Dual edge      106
Duet in (n + 1)-graph      175
E-move, $E^{ijk}_{r}$ -move      133
Equivalent 2-gems      99
Equivalent string presentations      55
Essential $u^{n}$ -class      15
Euler characteristic      105
Expanded gist      54
F-move, $F^{i}_{r}$ -move      133
Face      21
Face of a graph embedded in a surface      17
Framed link      5 77
Free reduction      73
Fusible edge      172
Fusion at two vertices      100
Genus of a Heegaard splitting      66
Geometric dual      106
Handle      120
Handle free, 3-manifold      177
Handle slide      270
Handleboly      66
Heegaard diagram      66
Heegaard splitting      66
Horizontal move      15
ij-gon      16
Incidence matrix of a digraph      106
Intersection numbers      243
Involution      32
Involved colors in a dipole      38
Involved colors in dipoles      3
Irreducible 3-manifold      125
Isotopy, ambient      269
Isotopy, regular      269
L(p,q)      31
Linking matrix      264
Loop in a graph      106
Medial of a plane graph      256
monopole      13 142
Move $A^{i}_{r}$       131
Move $B^{i}_{r}$       131
Move $C^{i}_{r}$       132
Move $D^{ij}_{r}$       132
Move $E^{ijk}_{r}$       133
Move $F^{i}_{r}$       133
Mutability of a $TS_{\rho}$ -class      189
n-residue      2
Of a cellular embedding      21
Orientable prime manifold      103
Perfect group      4
Pillow      39
Pillow move      39
Planar 3-manifold      255
Preserving the orientation      53
Prime 3-manifold      113
q-deformed quantum factorial      261
q-deformed quantum integer      260
Quantum invariants      224
Quartet      120
Quaternionic space      34
r-admissible state      262
Reduced adjacency matrix of a 3-gem      42
Reducible 3-manifold      125
Ribbon move      270
Rigid $S^{2}$ -gems      172
Rigid 3-gem      6 11 127
Root vertex of a 3-page      130
Root vertex of a ladder      130
Root vertex of a quasi-cluster      130
Root vertex of a quasi-cube      129
Root vertex of a TS-configuration      129
Size of a 3-gem      29
State      262
String presentation      5 52
String presentation equivalent to a 3-gem      55
String presentation for $\mathcal{S}(3, 3, 2, 1)$       55
String presentation for a 3-gem      30
Strong component of a directed graph      155
Superattractor for a 3-manifold      4
Surface induced by 2-gem      97
Switching of a $\rho$ -pair      40
Switching of a rho-pair      10
Symmetric space      118
System of meridian disks in a handlebody      68
Tidy matrix for a (3 + 1)-graph      147
Triball      20
Trio in (n + 1)-graph      107
TS-configuration, 3-page      13
TS-configuration, ladder      12
TS-configuration, quasi-cluster      12
TS-configuration, quasi-cube      11
TS-configurations      129
TS-moves      11
U-move      13
Walking triplet      100

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