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Start of Citation[PU]Institute of Physics Publishing[/PU][DP]1990[/DP]End of Citation

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Page 497

Index

A

A-genus, 396

Abelian group, 616

Abrikosov lattice, 24

Action, 177

effective, 180

free, 180, 319

transitive, 180, 319

Adjoint, 46

Fredholm operator, 409

Adjoint map, 185, 330

Adjoint representation, 185

Affine connection, 20910

AharonovBohm effect, 3569

Algebraic variety, 272

Almost complex manifold, 297300

Almost complex structure, 2756, 287, 297300

AmbroseSinger theorem, 343

Analytical index, 409

AndersonToulouse vortex, 126

Anomaly, 434

Abelian anomaly, 43441, 45860

non-Abelian anomaly, 434, 4414, 4556, 45860

parity, 45660

Antiholomorphic vector, 277

field, 277

Anti-self-dual solution, 18, 360

Antisymmetriser, 158

Arithmetic genus, 416

Associated fibre bundle, 325

AtiyahPatodiSinger index theorem, 4303, 459

AtiyahSinger index theorem, 41213, 440

Atlas, 133

compatible, 134

Axial anomaly, 438

B

Barycentric coordinate, 66

Base point, 90

Base space, 303, 305

BecchiRouetStora (BRS) operator, 4457

BelavinPolyakov monopole, 20

Beltrami differential, 484, 488

Bernoulli number, 389

Berry's connection, 366

Berry's curvature, 366

Berry's phase, 2930, 36471, 453

Betti number, 86, 195, 199, 257, 288, 296

Bianchi identity, 13, 162, 22930, 246, 264

principal bundle, 345, 362

Bidegree, 278

Biholomorphic, 273

Biholomorphism, 273

Bijective, 36

BornOppenheimer approximation, 367

BoseEinstein condensation, 24

Bott periodicity theorem, 121

Boundary, 50

group, 73, 189

of manifold, 134

of oriented simplex, 723

of singular simplex, 189

operator, 72

Bouquet, 107

Brouwer fixed-point theorem, 129

Bundle map, 309

C

CalabiYau manifold, 2912

CalliasBottSeely index theorem, 433

Canonical line bundle, 314

Canonical local trivialisation, 320, 332

Canonical one-form, 176



Page 498

Canonical system of curves, 83

Cartan's homotopy formula. 399

Cartan's structure equation, 245

principal bundle. 342

CauchyRiemann relation, 235, 265

Cech *cochain, 403

Cech cohomology group, 403

Chain, 71, 188

complex, 73

group, 71, 188

Characteristic class, 373, 379

Chart, 133

Chern character, 3857

second, 362

total, 385

Chern class, 3802

first, 286

total, 380

ChernSimons form, 362, 397, 448

ChernWeil theorem, 3768

Chiral current, 437

Chiral symmetry, 434

Chirality, 421

Christoffel symbol, 27, 214

Classifying space, 384

Clifford algebra. 421

Closed, 50

Closed form, 162, 255

Closure, 50

Coboundary group, 191, 281

Co-closed, 255

Cocycle group, 191, 281

Coexact, 255

Cohomologous, 192

Cohomology ring, 199, 373

Cokernel, 409

Commutative, 36

Commutator subgroup, 113

Compact, 512

Compatibility condition,

local connection, 3345

Complex,

conjugate, 2734, 277

Euclidean space, 289

form, 2778

manifold, 2656, 462

structure, 266

torus, 26771

vector field, 274

Complexification, 2735

Composite map, 36

Conformal

group, 235

invariance, 469

structure, 235

transformation. 234

Conformal Killing vector (CKV), 243, 474, 487

Conformally flat. 238, 264

Conformally related, 2359

Conjugacy class, 42

Conjugate, 42

Conjugate vector field. 274

Connected, 523

arcwise, 52, 94

simply, 52, 99

Connected sum, 58

Connection,

principal bundle, 32931

Riemannian geometry, 20710

Connection coefficient, 210

transformation property, 21213

Connection one-form,

Riemannian geometry, 245, 261


Constant map, 36

Continuous map, 4950

Contorsion, 214

Contractible, 98

Contraction (homotopy). 98

Contraction (tensor), 48

vector space, 48

Cooper pair, 24

Coordinate, 133

function, 133

neighbourhood, 133

Coordinate basis, 145

Coordinate bundle, 306

Coset, 42

Cosmological constant, 259

Cotangent bundle, 315

Cotangent space, 146

Cotangent vector, 146

Covariant derivative, 11

associated vector bundle, 3467



Page 499

Covariant derivative (cont.)

Hermitian geometry, 2845


Riemannian geometry, 208, 21112

Covering, 51

open, 51

Covering group, 117

Covering space, 117

Critical dimension, 480

Critical temperature, 20

Cross cap, 88

Cross section, 305, 307

Curvature two-form



Curve, 142

Cusp form, 491

Cycle, 73, 189

group, 73, 189

Cyclic group, 38, 646

finite, 64

infinite, 64

D

-closed*, 292

-cohomology* group, 281, 2926

-exact*, 293

-harmonic*, 294

-operator*, 280, 293

adjoint, 293

de Rham cohomology group, 162, 1913, 2567, 362, 3734

de Rham complex, 162, 196, 411, 41314

de Rham's theorem, 194

Dedekind h-function, 490

Defect, 122

line, 1234

point, 124

ring, 125

surface, 122

Deformation retract, 97

Degree, 100

Dehn twist, 271, 470

Derrick's theorem, 34

Descent equation, 449

Diffeomorphic, 141

Diffeomorphism, 141, 469

Differentiable, 140

structure, 134

Differential form, 15860

Differential map, 147

Dilatation vector, 243

Dimension, 43

Dimensional ladder, 458

Dirac genus, 396, 423

Dirac matrix, 244, 420

Dirac operator, 422

Dirac string, 15

Director, 25

Disconnected, 52

Discriminant, 491

Disgyration, 126

Dolbeault complex, 281, 415

twisted, 416

Dolbeault operator, 280

Domain, 35

Domain wall, 122

Dual basis, 44

Dual bundle, 316

Dual field tensor, 13

Dual vector, 45, 146

Dual vector space, 44, 145

Duality transformation, 2502

E

h-invariant, 42930, 458

Edge group, 105

Edge loop, 104

Edge path, 104

Effective action, 7

Ehresmann connection, 332, 446

Einstein equation, 28, 259

EinsteinHilbert action, 2579

Einstein summation convention, 1

Einstein tensor, 28, 231, 259

Eisenstein series, 490

Elliptic complex, 41011

Elliptic operator, 4078

Embedding, 149, 262

Energymomentum tensor, 28, 259

Equivalence class, 38

Equivalence relation, 38

Equivalent bundle, 306, 310, 312

Euclidean metric, 205

Euler characteristic, 569, 86, 195, 198, 203, 257, 393, 411, 468





Page 500

Euler class, 3935

EulerPoincar theorem, 86

Euler's theorem, 57

Even bundle, 411

Exact form, 162

Exponentiation, 152

Extension, of a linear operator, 274

Exterior derivative, 1602

adjoint operator, 253

Exterior product, 159

F

Face, 66

proper, 66

FaddeevPopov (FP) ghost, 4457

Fibre, 3045

dimension, 313

metric, 316

Fibre bundle, 3058

reconstruction, 3089

Field strength, 344

Field tensor, 1013

electromagnetic, 10, 162

YangMills, 12

Finitely generated Abelian group, 646

fundamental theorem, 65

Form, 158

Frame, 315

Frame bundle, 3256, 349

Lorentz, 326

Fredholm operator, 409

Free Abelian group, 64

Free group, 1024

FubiniStudy metric, 290, 387

Fuchsian group, 486

Fujikawa's method, 43641

Function, 143

Fundamental group, 939

polyhedron, 10213

Fundamental vector field, 330

G

G bundle, 319

Gauge potential, 335

Gauge slice, 469

Gauge theory, 1014

Abelian, 10, 3545

and principal bundle, 35464

non-Abelian, 12, 359

three-dimensional, 401

Gauge transformation, 10, 335

GaussBonnet theorem, 59, 394, 414

Gauss' theorem, 191

General relativity, 279, 257

Generating functional, 6, 7, 9

Generator, 64

Abelian group, 64

free set of, 102

Genus, 40, 461

Geodesic, 211

Livi-Civita connection, 2237

GinzburgLandau free energy, 22

condensation, 22

gradient, 22

Grassmann variable, 8, 33, 438

Grassmannian manifold

complex, 2712, 384

real, 1389, 1824

H

Handedness, 165

Harmonic form, 2557, 294, 417

Harmonic map, 263

Hausdorff space, 50

Heat equation, 426

Heat kernel, 425, 466

regularisation, 439

Helicity, 463

Hermitian connection, 285, 353

Hermitian manifold, 282

Hermitian metric, 2812

Hermitian structure, 353

Higgs field, 13

Higher homotopy group, 11318

Hirzebruch L-polynomial, 396, 420

HirzebruchRiemannRoch theorem, 416

Hirzebruch signature, 397, 417

theorem, 397, 420

Hodge decomposition theorem, 2556

Hodge diamond, 2956

Hodge number, 295, 416

Hodge star operation, 2502


inverse, 252



Page 501

Hodge's theorem, 257


Holomorphic, 265

form, 280, 295

function, 273

map, 273

tangent bundle, 352

vector, 277

vector bundle, 352

vector field, 277

Holonomy group,

Berry's phase, 368

Khler manifold, 2912


restricted, 340


Homeomorphism, 539

Homogeneous coordinate, 137, 271

Homogeneous space, 181

Homologous, 75

Homology class, 75

Homology group, 7484

general property, 847

singular, 189

Homomorphism, 37

Abelian group, 62

fundamental theorem, 63

Homotopic, 91, 96, 114, 201, 312, 328

Homotopy, 913, 96, 114

class, 93, 114

equivalence, 96

inverse, 96

Homotopy group, 93, 11318

Homotopy operator, 399

Homotopy type, 556, 59, 96

Hopf invariant, 328

Hopf map, 3224

Horizontal lift, 3369, 346

Horizontal subspace, 3302

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