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Brylinski J.-L Ч Loop Spaces, Characteristic Classes and Geometric Quantization
Brylinski J.-L Ч Loop Spaces, Characteristic Classes and Geometric Quantization

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Ќазвание: Loop Spaces, Characteristic Classes and Geometric Quantization

јвтор: Brylinski J.-L

јннотаци€:

Develops a Chern-Weil theory of characteristic classes of gerbes, fiber bundles whose fibers are groupoids, which arise naturally in the geometric aspects of mathematics and physics. Includes a self-contained introduction to the theory of sheaves and their cohomology, line bundles, and geometric prequantization. Written for topologists, geometers, Lie theorists, and mathematical physicists at a graduate or professional level.


язык: en

–убрика: ћатематика/√еометри€ и топологи€/јлгебраическа€ и дифференциальна€ топологи€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1993

 оличество страниц: 161

ƒобавлена в каталог: 12.11.2004

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$C/\Lambda$-bundle      105Ч110
3-curvature      178 214Ч219
Abelian variety      102
Abutment of a spectral sequence      17
Action functional      239Ч243
Acyclic      22 23
Affine space of connections      71 73
Almost-complex structure on the space of knots      126Ч135
Anti-holomorphic involution of the space of knots      135 138
Associated character      229
Associated sheaf      4
Associated sheaf, of categories      193Ч194
Associated vector bundle to a group representation      170
Associativity constraint      271
Band of a gerbe      195Ч203
Bar complex      116Ч117
Based path space      220
Based singular knot      118
Basic differential form      61
Beilinson, A. and Bernstein, J.      232
Binormal vector      140
Blow-up      64
Borel construction      119
Bott Ч Virasoro group      100
Bounded below      20Ч24
Brauer group (topological)      166
Breen, L.      271Ч272
Bundle automorphism, bundle diffeomorphism for a line bundle      94
Canonical 3-form on a compact Lie group      224Ч225
Cartan filtration of differential forms      59 60 61
Cartan subalgebra      224
Cartan Ч Leray spectral sequence      61
Cartan, E.      223
Cartan, H.      1
Cech coboundary      25
Cech cocycle      25
Cech cohomology      25
Cech complex      25
Central extension, of a group of symplectomorphisms      100Ч103
Central extension, of a Lie algebra of hamiltonian vector fields      89Ч93
Central extension, of a loop group      247Ч249
Cheeger Ч Simons differential characters      50
Chern Ч Simons classes      50 276Ч277
Chern Ч Simons field theory      249
Christofel symbol      145
Circle bundle over the space of knots      121Ч126
Coadjoint orbit      157
Cocycle condition      185Ч187
Cocycle for Lie algebras      88Ч89
Cohomology of sheaves      11
Cohomology with support      264 268
Compact Lie group      223Ч231
Compact operators, Banach algebra of      161
Compatible connections      169Ч170
Complementary degree      15
Complex Lie group      226Ч227
Complex of sheaves      9
Conformal structure on a three-manifold      126
Connection 1-form on a $C^{*}$-bundle      72
Connection compatible with the holomorphic structure      80
Connection form on the space of knots      123Ч126
Connection on a line bundle      70
Connection on a principal bundle      121Ч126 168Ч171
Connection-preserving vector field      91
Connective structure      206Ч211
Constant sheaf      6
Continuous Heisenberg chain      140Ч141
Contracted product of gerbes      200
Contracted product of spaces with $C^{*}$-action      63
Contracted product of torsors      191
Convergence of a spectral sequence      17
Coroot      224
Covering (open)      2 24
Crossed product algebra      179
Cup-product      29 30
Curvature for a principal bundle      121Ч126 169Ч175
Curvature of a connection on a line bundle      74
Curvature of bundles over the space of knots      123Ч126
Curving of a connective structure      211Ч219
Cyclic complex      119
Cyclic homology      119Ч120
de Rham algebra      117
De Rham cohomology      36
de Rham complex      35 36
Degenerate (at $E_{r}$)      17
Deligne cohomology      46Ч54
Deligne complex      47 53
Deligne Ч Beilinson cohomology      54
Deligne Ч Beilinson cohomology and holomorphic line bundles      80
Deligne, P.      205
delta function (of Dirac)      264
Descent category      189 193Ч194
Descent datum, descent isomorphism      186Ч191
Determinant line bundle      102
Diffeological group      108
Diffeology      107
Diffeomorphisms of the circle      100 111
Differential character      see УCheeger Ч Simons differential characterФ
Dilogarithm      83
Dirac monopole      257Ч277
Direct image (of a sheaf)      55
Direct limit of categories      192Ч194
distribution      113Ч114
Distribution, of tangent planes      139
Dixmier Ч Douady sheaf of groupoids      203
Dixmier Ч Douady theory      158Ч168
Dolbeault differential      129
Double complex      13 14 18 19
Drinfeld, V.I.      131
Elliptic object      241
Epimorphism of sheaves      7
Equivalence, categories      63Ч64
Equivalence, of gerbes      199Ч200
Equivariant, cohomology      118Ч120
Equivariant, line bundle      228
Equivariant, Picard group      228Ч231
Equivariant, sheaf of groupoids      269 275Ч277
Exact sequence of groups or sheaves of groups      6
Exact sequence, of Lie algebras      92
Exact sequence, of sheaves of nonabelian groups      160
Exhaustive filtration      13
Family of symplectic manifolds      178Ч181
Fiber integration      61
Fiberwise connection      203Ч205
Filtering degree      15
Filtration, first      15
Filtration, of a complex      13
First Chern class      66
First degree      see УFiltering degreeФ
Flabby sheaf      38
Flat line bundle      69Ч70
Flat sheaf of groupoids      217Ч218
Formally integrable complex structure      129
Free loop space      110
Frenet frame      127
Function of hamiltonian type      87
Gauge      262Ч263
Gauge, transformation      262Ч263
Gawedzki, K.      250Ч253
Gel'fand, I.M. and Fuks, D.B.      100
Generalized function      113Ч115
Generalized section      113Ч115
Geodesics      135 150
Gerbe      196Ч205
Germ      3
Giraud, J.      196
Global sections (of a sheaf)      7
Godement, R.      23
Good covering      28 29
Goodwills Ч Jones theory      119Ч120
Gotay, M., Lashof, R., Sniatycki, J. and Weinstein, A.      181
Griffiths intermediate jacobian      54
Grothendieck, A.      182Ч183 191Ч192
Group cocycle      270Ч277
Groupoid      172
Groupoid, with tensor product      270Ч277
Gysin exact sequence      61
Hamiltonian      257Ч261
Hamiltonian, vector field      86 257Ч258
Hasimoto, R.      141Ч144
Heisenberg group      102 166Ч168
Hermitian, connection on a line bundle      79Ч80
Hermitian, line bundle      67Ч68
Hermitian, metric on a line bundle      67Ч68
Higher direct image sheaf      55Ч61
Hilbert space      161
Hilbert Ч Schmidt operators      99
Hitchin, N.      135
Hochschild homology      116Ч120
Hodge cohomology class      54
Hodge to de Rham spectral sequence      53
Holomorphic, connection on a holomorphic line bundle      80Ч84
Holomorphic, Dixmier Ч Douady sheaf of groupoids      218Ч219 226Ч227
Holomorphic, line bundle      68
Holonomy, of a Dixmier Ч Douady sheaf of groupoids      237Ч243
Holonomy, of a line bundle      234Ч236
Holonomy, of a principal bundle      114Ч115
Homogeneous coordinates      64
Homotopy      9 30
Hopf fibration      134
Horizontal lift      90
Horizontal lift of a vector field on the space of knots      121Ч126
Horizontal section of a line bundle      74
Horizontal tangent bundle      72
Hypercohomology of a complex of sheaves      21 22 23 33 34
Hypercohomology spectral sequence      24
ILH group      94
ILH space inverse limit of Hilbert      40
Immersion      115Ч116
Infinite-dimensional, algebra bundle      158Ч168
Infinite-dimensional, Grassmann manifold      99
Infinite-dimensional, manifold      35
Injective, group      8
Injective, resolution of a sheaf      10 11 12
Injective, sheaf      8
Integrable almost-complex structure      128
Inverse image of a sheaf      36
Isomorphism of line bundles      62Ч63
Kac Ч Moody group      248
Killing form      222Ч223
Knop.F., Kraft, H. and Vust, T.      231
Kostant central extension      see УCentral extension of a group of symplectomorphismsФ
Kostant Ч Souriau prequantization      93
Kostant, B., introduction      77Ч80
Lagrangian submanifold of the space of knots      138
Laurent series      26
LeBrun, C.      131 135
Left-exact      7
Lempert, L.      128 131
Leray spectral sequence      54 57 180Ч181
Leray, J.      1
Lie algebra, cocycle      88Ч90 276Ч277
Lie algebra, cohomology      222Ч223 276Ч277
Lindelof space      41
Line bundle      62
Line bundle, on the space of knots      243Ч247
Line bundle, with connection      76Ч77
Local homeomorphism      183Ч184
Locally constant      58
Locally convex topological vector space      35
Loop group      6Ч14
Lorentz force      260
Lorentzian metric      131
Magnetic, field      260Ч263
Magnetic, monopole      see Уmonopole (Dirac)Ф
Marsden J. and Weinstein, A.      126Ч127 137 156
Maxwell equations      260
Meromorphic function      26
Mickelsson, J.      247Ч249
Mixed complex      119
Moment map      153Ч155
Momentum (vector)      257
Monodromy representation      58
Monomorphism of sheaves      7
Morphism of sheaves      3
Moser, J.      156
Mumford, D.      102
Nerve of a covering      29
Nijenhuis tensor      128Ч130
Nonabelian sheaf cohomology degree      1 158Ч168
Nonlinear Schroedinger equation (NLS)      141Ч144
Normalization of a singular knot      113
Null-geodesic      131Ч133
O'Neill, B.      145Ч147
Observable      258
Omori, H.      93
Palais, R.      229
Paracompact (space)      32
Parallel transport, for line bundles      95
Parallel transport, for sheaves of groupoids      254Ч256
Partial connection      97
Partition of unity      39 42
Path space      96
Pentagon (of MacLane)      271
Perfect (group)      95
Picard group      69 271
Planck constant      258
Plaque of a diffeology      108
Poincare lemma      35
Pointed set      160
Poisson bracket      88
Pontryagin class (first)      256
Potential      257Ч259
Potential, vector      260Ч263
Presheaf      1
Presheaf, of categories      191Ч194
Pressley, A., and Segal, G.      99Ч100 224
Principal bundle      121Ч126 158
Projective, automorphism      165
Projective, Hilbert space      165
Projective, space bundle      165
quantum mechanics      258
Quasi-isomorphism      24
Real-analytic knots      131Ч133
Regular filtration      13
Relative differential form      59
Resolution (of a sheaf)      10
Restriction map      1
Richter, B.      225
Right derived functor      8
Root      224
Scalloped      40 41
Schroedinger equation      258Ч259
Second degree      14
Second filtration      15
Section (of a presheaf)      1 2
Segal localization      124Ч125
Segal reciprocity law      249
Segal, G. and Wilson, G.      99
Sheaf      2
Sheaf, cohomology groups      11
Sheaf, of categories      191Ч195
Sheaf, of groupoids      195
Singular knot      112
Sinh invariant      271 275
Skyscraper sheaf      8
Smale, S.      116
Smooth Deligne cohomology      47
Smooth Deligne cohomology and gerbes      214Ч217
Smooth Deligne cohomology and holonomy      234Ч236 250Ч254
1 2
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