Навигация

Архив выставки новых поступлений | Отечественные поступления | Иностранные поступления | Сиглы
ОбложкаAkbulut S. 4-manifolds. - Oxford: Oxford University Press, 2016. - xii, 262 p.: ill. - Bibliogr.: p.245-260. - Ind.: p.261-262. - ISBN 978-0-19-878486-9
Шифр: (И/B18-A29) 02

 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
Preface ....................................................... vii
1  4-manifold handlebodies ...................................... 1
   1.1  Carving ................................................. 4
   1.2  Sliding handles ......................................... 6
   1.3  Canceling handles ....................................... 8
   1.4  Carving ribbons ........................................ 10
   1.5  Non-orientable handles ................................. 14
   1.6  Algebraic topology ..................................... 16
2  Building low-dimensional manifolds .......................... 19
   2.1  Plumbing ............................................... 21
   2.2  Self plumbing .......................................... 22
   2.3  Some useful diffeomorphisms ............................ 23
   2.4  Examples ............................................... 24
   2.5  Constructing diffeomorphisms by carving ................ 29
   2.6  Shake shce knots ....................................... 32
   2.7  Some classical invariants .............................. 33
3  Gluing 4-manifoIds along their boundaries ................... 37
   3.1  Constructing - M ̮ ƒ N by the upside down method ........ 37
   3.2  Constructing - M ̮ ƒ N and M(ƒ) by the cylinder method
        (roping) ............................................... 39
   3.3  Codimension zero surgery M → M' ........................ 42
4  Bundles ..................................................... 43
   4.1  T4 = T2 × T2 ............................................ 43
   4.2  Cacime surface ......................................... 45
   4.3  General surface bundles over surfaces .................. 52
   4.4  Circle bundles over 3-manifolds ........................ 52
   4.5  3-manifold bundles over the circle ..................... 53
5  3-manifolds ................................................. 55
   5.1  Dehn surgery ........................................... 56
   5.2  Prom framed links to Heegaard diagrams ................. 57
   5.3  Gluing knot complements ................................ 59
   5.4  Carving 3-manifolds .................................... 61
   5.5  Rohlin invariant ....................................... 62
6  Operations .................................................. 64
   6.1  Gluck twisting ......................................... 64
   6.2  Blowing down ribbons ................................... 67
   6.3  Logarithmic transform .................................. 68
   6.4  Luttinger surgery ...................................... 69
   6.5  Knot surgery ........................................... 71
   6.6  Rational blowdowns ..................................... 74
7  Lefschetz fibrations ........................................ 78
   7.1  Elliptic surface E(n) .................................. 80
   7.2  Dolgachev surfaces ..................................... 81
   7.3  PALFs .................................................. 84
   7.4  ALFs ................................................... 87
   7.5  BLFs ................................................... 92
8  Symplectic manifolds ........................................ 95
   8.1  Contact manifolds ...................................... 96
   8.2  Stein manifolds ........................................ 98
   8.3  Eliashberg's characterization of Stein ................. 99
   8.4  Convex decomposition of 4-manifolds ................... 101
   8.5  T4 = |BLF| ............................................ 103
   8.6  Stein = |PALF| ........................................ 106
   8.7  Imbedding Stein to symplectic via PALF ................ 107
   8.8  Symplectic fillings ................................... 109
9  Exotic 4-manifolds ......................................... 112
   9.1  Constructing small exotic manifolds ................... 112
   9.2  Iterated 0-Whitehead doubles are non-slice ............ 116
   9.3  A solution of a conjecture of Zeeman .................. 119
   9.4  An exotic fig.14 .......................................... 119
   9.5  An exotic non-orientable closed manifold .............. 120
10 Cork decomposition ......................................... 123
   10.1 Corks ................................................. 125
   10.2 Anticorks ............................................. 130
   10.3 Knotting corks ........................................ 132
   10.4 Plugs ................................................. 133
11 Covering spaces ............................................ 138
   11.1 Handlebody of coverings ............................... 138
   11.2 Handlebody of branched coverings ...................... 141
   11.3 Branched covers along ribbon surfaces ................. 147
12 Complex surfaces ........................................... 150
   12.1 Milnor fibers of isolated singularities ............... 150
   12.2 Hypersurfaces that are branched covers of fig.2fig.32 ........ 153
   12.3 Handlebody descriptions of Vd ......................... 155
   12.4 ∑(a,b,c) .............................................. 158
13 Seiberg-Witten invariants .................................. 163
   13.1 Representations ....................................... 164
   13.2 Action of λ*(Х) on W* ................................. 166
   13.3 Dirac operator ........................................ 171
   13.4 A special calculation ................................. 173
   13.5 Seiberg-Witten invariants ............................. 174
   13.6 S-W when b2+(X) = l .................................... 181
   13.7 Blowup formula ........................................ 182
   13.8 S-W for torus surgeries ............................... 182
   13.9 S-W for manifolds with T3 boundary .................... 183
   13.10 S-W for logarithmic transforms ....................... 185
   13.11 S-W for knot surgery ХK .............................. 186
   13.12 S-W for S1 × YЗ ...................................... 189
   13.13 Moduli space near the reducible solution ............. 191
   13.14 Almost complex and symplectic structures ............. 193
   13.15 Antiholomorphic quotients ............................ 200
   13.16 S-W equations on fig.1 × YЗ .............................. 201
   13.17 Adjunction inequality ................................ 202
14 Some applications .......................................... 206
   14.1 10/8 theorem .......................................... 206
   14.2 Cappell-Shaneson homotopy spheres ..................... 210
   14.3 Flexible contractible 4-manifolds ..................... 219
   14.4 Some small closed exotic manifolds .................... 223
        14.4.1 An exotic fig.2fig.32 # 3fig.2fig.32 ......................... 223
        14.4.2 An exotic
              fig.2fig.32 # 2fig.2fig.32 .................................... 234
        14.4.3 Fintushel-Stern reverse engineering ............ 243
References .................................................... 245
Index ......................................................... 261


Архив выставки новых поступлений | Отечественные поступления | Иностранные поступления | Сиглы
 

[О библиотеке | Академгородок | Новости | Выставки | Ресурсы | Библиография | Партнеры | ИнфоЛоция | Поиск]
  Пожелания и письма: branch@gpntbsib.ru
© 1997-2024 Отделение ГПНТБ СО РАН (Новосибирск)
Статистика доступов: архив | текущая статистика
 

Документ изменен: Wed Feb 27 14:30:30 2019. Размер: 10,121 bytes.
Посещение N 621 c 22.01.2019