Nash C., Sen S. — Topology and geometry for physicists :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Nash C., Sen S. — Topology and geometry for physicists

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Topology and geometry for physicists

Авторы: Nash C., Sen S.

Аннотация:

Applications from condensed matter physics, statistical mechanics and elementary particle theory appear in the book. An obvious omission here is general relativity — we apologize for this. We originally intended to discuss general relativity. However, both the need to keep the size of the book within the reasonable limits and the fact that accounts of the topology and geometry of relativity are already available, for example, in The Large Scale Structure of Space-Time by S. Hawking and G. Ellis, made us reluctantly decide to omit this topic.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1983

Количество страниц: 319

Добавлена в каталог: 22.12.2013

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

Предметный указатель

$\alpha$ -planes      285—289
$\alpha$ -planes and anti-self-dual connections      288—289
$\alpha$ -planes and complex projective space      287—288
$\beta$ -planes      285—288
Affine transformation law      178 181
Algebraic geometry      289 294
Almost complex structures      170—171
Almost Hamiltonian structures      165—167 171
Anti-self-duality      259 285—297
Anti-self-duality and $\alpha$ -planes      286 288—289
Anti-self-duality and holomorphic structure      292—297
Anti-self-duality, definition of      259
Atiyah — Singer index theorem      220 280
Atiyah — Singer index theorem and instantons      280
Atlas      26 36—37
Betti number      91
Bianchi identities      182—183 190 192 257
Biholomorphic      221
Bogomolny equation      298—301
Bohm — Aharanov effect      301—302
Boundary      86
Boundary operator      84 121—123
Brouwer fixed point theorem      6
Calculus on manifolds      37—48
Canonical transformations      169
Cap product      139
Cauchy's residue theorem      1—2
Chain      84
Characteristic classes      see "Names of specific characteristic classes"
Characteristic classes in general      200—225
Characteristic classes in terms of curvature and invariant polynomials      206—211
Characteristic classes of a manifold      219
Characteristic classes, calculation of      213—217
Characteristic classes, formulae obeyed by      219—221
Characteristic classes, universal      221
Characteristic numbers of a manifold      219
Chart      26 36—37
Chern character      220
Chern classes      204—210 213—215 217—220
Chern classes in terms of curvature      207—210
Christoffel symbol      187
Closed form      123
Closed set      13—15 17
Cohomology      120—139
Cohomology and de Rham cohomology      122—138
Cohomology and non-compactness      136—137
Cohomology and non-orientability      136—137
Cohomology groups      120
Cohomology groups for $S^{n}$       136
Cohomology groups for $T^{n}$       136
Cohomology groups, calculation of      127—136
Cohomology groups, de Rham      123—139
Cohomology groupsfor a general manifold      136
Cohomology versus homology      138—139
Cohomology with real coefficients      121
Compact set      16—19
Compactness      16—19 22—23
Compactness, topological invariance of      22—23
Complex orthogonal group      285—288
Complex projective space      138 217 287—288
Complex projective space and $\alpha$ -planes      287—288
Complex projective space and spin structures      217
Complex structures      170—171 291
Conformal invariance      259—260
Conformal invariance of the * operation      260
Conformal invariance of the action S      260
Connected set      19—20
Connectedness      19—20 22—23 53
Connectedness, path      53
Connectedness, topological invariance of      22—23
Connection form      177—178
Connections      174—198 256—303
Connections in the tangent bundle      184—194
Connections, Levi — Civita      191—194
Connections, Maxwell      196—198 297—298
Connections, physical significance of      301—302
Connections, Yang — Mills      194—196 256—303
Continuity      9—12
Continuous deformation      9 25
Contractibility of Gl(n,C) to U(n)      163—164
Contractibility of Gl(n,R) to O(n)      162
Contractibility to a maximal compact subgroup      163
Contractible manifold      125—127
Contractible manifold, definition of      125
Contravariant vector      39—40
Cotangent bundle      150 166
Covariant derivative      174 179—180 183—187
Covariant exterior derivative      181—182
Covariant vector      39—40 42
Covering space      254
Critical point      227
Cup product      137—138
Cup product and ring structure of H*(M;R)      138
Curvature      179—181
Curvature and lack of commutativity of covariant differentiation      179—180
Curvature tensor      180—181 188
Curvature, dual of      183
CYCLE      86
defects      244—255
Defects, combination rule for line defects      249
Defects, crossing of line defects      251—253
Defects, definition of      246
Defects, stability of      246
Deformation      1
Deformation retract      64 135
Dense set      16
Diffeomorphism      49 221
Differentiable structures      49—50
Differentiable structures, different      49
Differential      40
Differential form      see "r-form"
Differential geometry      25—50 171—225
DIMENSION      23—24
Dimension, topological invariance of for $R^{n}$       23—24
Dimension, topological invariance of for a manifold      26
disconnected set      20
Dual      39—40
Dual basis      40
Dual of a linear map      39—40
Dual of a vector space      39
Dynamical system      8
Equivalence of T(M) and T*(M)      163
Euler class      204 210—211 215—217 220
Euler class and Pfaffian      211
Euler Lagrange equations      257
Euler — Poincare characteristic      140
Euler — Poincare formula      106
Exact form      123
Exact sequences      99 123
Exact sequences of a fibre bundle      253
Exact sequences of homology groups      99
Exact sequences of homotopy groups      115—116
Exact sequences, application of exact homology sequence      100—104
Exact sequences, theorem for four groups      100
Excision theorem      98
Exterior algebra      42
Exterior derivative      41—43 121—123
Fibre bundle      140—225
Fibre bundle, base space of      142
Fibre bundle, classification of      200—212
Fibre bundle, contraction of the base space of      159—165
Fibre bundle, definition of      142
Fibre bundle, fibre of      142
Fibre bundle, list of      151
Fibre bundle, local triviality of      142
Fibre bundle, principal      152—156 261
Fibre bundle, projection of      142
Fibre bundle, reconstruction from transition functions      144—147
Fibre bundle, reduction of the group of      159—165
Fibre bundle, section of      152—156

Fibre bundle, structure group of      142
Fibre bundle, total space of      142
Fibre bundle, transition functions of      142
Fibre bundle, triviality of      152—156
Fibre bundle, triviality of over a contractible base      161
Finitely generated group      90
Fixed points      4—8
Fixed points of an operator      6—8
Fixed points of the disc $B^{2}$       4—7
Flow of a vector field      169
Freely generated group      90
Functions      9—12
Functions with discontinuity      10—11
Functions, continuous      9
Fundamental group      51—78
Fundamental group of $D^{2}$       71
Fundamental group of $S^{1}$       71
Fundamental group of $S^{2}$       72
Fundamental group of a product $X \times Y$       77
Fundamental group of Klein bottle      76
Fundamental group of Moebius band      72
Fundamental group of projective plane      75
Fundamental group of torus $T^{2}$       74
Fundamental group, definition of      56
Fundamental group, dependence on base point      58
Fundamental group, non-abelian nature of      66
Fundamental group, the calculating theorem      68
Fundamental theorem of algebra      3
G-structures      163—171
G-structures, topological restrictions to existence of      164 167—171
Gauge potential      178 299 see
Gauge potential, static      299
Gauss — Bonnet theorem      140 223—225
Generators of an Abelian group      90
Geodesics      190—191
GL(n,R)      149—152
Global invariants and local geometry      221—225
Grassmann manifold      201 205—206
Grassmann manifold, complex      205
Grassmann manifold, oriented      205
Hamiltonian manifold      166
Hamiltonian structures      166—171
Hamiltonian structures and classical phase space      166
Hamiltonian structures and Hamilton's equations      168—169
Hausdorff space      27—28
hessian      227
Holes in a manifold and cohomology      131
Holomorphic structure      292—297
Holomorphic vector bundle      291—297
Homeomorphism      20—24 26 221—222
Homeomorphism and continuous deformation      20
Homeomorphism and equivalence classes      20—22
Homeomorphism as a continuous invertible map      23
Homology groups      79—108 120
Homology groups of $S^{1}$       89
Homology groups of $S^{n}$       104
Homology groups of a connected polyhedron      89
Homology groups of a contractible space      87
Homology groups of D2      87
Homology groups of projective plane      91
Homology groups, definition of      86
Homology groups, excision theorem of      98
Homology groups, simplicial      79
Homology groups, singular      107
Homology groups, torsion subgroup of      91
Homotopy      21—22 128—129 135 160—161 244—255 260—262
Homotopy and defects      244—255
Homotopy and instantons      260—262
Homotopy and pullback bundles      160—161
Homotopy group      109—119
Homotopy group Abelian nature for n>1      112
Homotopy group of $S^{n}$       118
Homotopy group, definition for n>1      111
Homotopy group, first      see "Fundamental group"
Homotopy of maps      21—22 128—129 135
Homotopy type      60
Homotopy, invariants      22
Hopf map      225
Horizontal lift      175 184 187 195
Horizontal subspace      175—177
Hurewicz Theorem      118
Induced bundle      see "Pullback bundle"
instantons      256—297
Instantons and absolute minima      263—265
Instantons and finite action      259—260
Instantons and holomorphic vector bundles      289—294
Instantons and Minkowski space      297
Instantons and the second Chern class      269—272
Instantons and twistor methods      283—288
Instantons with k=1      265—269
Instantons with k>1      272 278—282
Instantons, construction of from holomorphic vector bundles      295—296
Instantons, topology and boundary conditions      260—262
Integral curves      172
Integration of      44—48
Integration of r-forms      44—49
Invariant polynomials      207—210
Invariant polynomials, homogeneity of      207
Invariants      221—225
Invariants of complex structure      221—222
Invariants of differential structure      221—222
Invariants of topological structure      221—225
Isotopy      21
Jacobi identity      182
Jacobian determinant      34—35 46
Jacobian matrix      150—151
k-cell      231
K-theory      139
Killing form      256
Kunneth formula      105
Lagrangian      256
Landau theory      236
Lie derivative      171—174
Linear independence and vector fields      157—158
Liouvilles theorem      296
Local product      141—143
Loop      53
Loop, homotopy of      54
Loop, inverse of      54
Loop, product of      54
Lorentz structures      171
Manifold      25—50 137
Manifold, definition of      26
Manifold, infinite dimensional      49
Manifold, orientable      137
Manifold, pseudo-Riemannian      29
Manifold, Riemannian      29 46
Maxwell's equations      197 298
Metric      164
Metric space      28—29
Metric, signature of      164
Minkowski space      258 297
Minkowski space, compactified      297
Moebius strip      34—35 137 141—148 152—156
Moebius strip as a fibre bundle      141—148
Moebius strip, principal bundle associated with      152—156
Monopoles      297—303
Monopoles and holomorphic vector bundles      301
Monopoles, Abelian      297—298
Monopoles, topological charge of      299—300
Morse inequalities      229
Morse inequalities, proof of      233—236
Morse lemma      229
Morse theory      49 227—243
Multi-instantons      272 278—282
N-loop      109
n-loop, homotopy of      110
n-loop, product of      110
Neighbourhoods      13
Nematic liquid crystal      250

1 2

О проекте