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Kashiwara M., Schapira P. — Sheaves On Manifolds
Kashiwara M., Schapira P. — Sheaves On Manifolds

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Название: Sheaves On Manifolds

Авторы: Kashiwara M., Schapira P.

Аннотация:

This book is devoted to the study of sheaves by microlocal methods..(it) may serve as a reference source as well as a textbook on this new subject. Houzel's historical overview of the development of sheaf theory will identify important landmarks for students and will be a pleasure to read for specialists. Math. Reviews 92a (1992). The book is clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics.(...)The book can be strongly recommended to a younger mathematician enthusiastic to assimilate a new range of techniques allowing flexible application to a wide variety of problems.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 514

Добавлена в каталог: 18.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\gamma$-closed      161
$\gamma$-open      161
$\gamma$-topology      161
$\mathbb{C}^{\times}$-conic      344
$\mu hom$      202
$\mu$-condition      334
$\mu$-filtration      337
$\mu$-stratification      334
Abelian category      26
Additive (category, functor)      26
Adjoint functor (right, left)      69
Analytic set ($\mathbb{C}$-)      344
Antidistinguished triangle      40
Antipodal map      169
Associated coordinate system (on the cotangent bundle)      481
Associated sheaf (to a presheaf)      86
Associated simple complex (to a double complex)      55
Bicharacteristic (curve, leaf)      271 482
Biconic set      242
Biconic sheaf      168
Bifunctor      56
Boundary operator      369
Boundary value      467
Bounded complex (from below, above)      31
c-soft dimension      133
c-soft sheaf      104
Can      352
Canonical 1-form      481
Cartesian square      106
Category      23
Cauchy problem      454
Cauchy residues formula      183
Cauchy — Kowalevski Theorem      453
Cauchy — Riemann system      468
Cech cohomology      125
Characteristic class (of a sheaf, of $\phi$)      362 390
Characteristic cycle      377
Characteristic variety (of a $\mathscr{D}$-module)      449
Clean (map)      190
Cocycle condition      487
Cofinal      81
Coherent      443
Cohomological dimension (of a left exact functor)      75
Cohomological functor      39
Cohomologically constructive complex      158
Cohomology      32
Coimage      28
Cokernel      28
COMPLEX      30
Conic set (in a vector bundle)      169 344 483
Conic sheaf      167
Conormal bundle      481
Constant sheaf      90
Constructive function      398
Constructive sheaf ($\mathbb{R}$-, $\mathbb{C}$-, $\mathbb{S}$-)      322 339 347
Contact transformation      483
Contravariant      25
Convex set (in a vector bundle)      169
Convolution (of sheaves, of constructive functions)      135 409
Cotangent bundle      481
Covariant      25
Cup product      134
Curve selection lemma      327
de Rham complex      127
Derived category      45
Derived functor (right, left)      50 52
Desingularization theorem      328
Differential (of a complex)      31
Differential operators (ring of)      448
Direct image (of a $\mathscr{D}$-module)      453
Direct image (of a microfunction)      470
Direct image (of a sheaf)      90
Direct image with proper supports      103
Direct sum      27
Direct summand      70
Directed ordered set      63
Distinguished triangle      35
Dolbeault complex      128
Double complex      54
Dual (of a complex of sheaves)      148
Dualizing complex (relative)      148
Elliptic system      468
Enough injectives (projectives)      48
Epimorphism      24
Equivalence of categories      25
Euler class      179
Euler morphism      406
Euler vector field      241 482
Euler — Poincare index      240 361
Exact (left, right) functor      29 30
Exact sequence      29
Expanding space      395
Extended contact transformation      292
External tensor product      97
F-acyclic      75
F-injective      50
F-projective      52
f-soft sheaf      140
Filtered ring (and module)      445 446
Filtrant category      62
Final object      24
Finer (covering)      334
Five lemma      72
Flabby dimension      98
Flabby sheaf      98
Flat module      77
Flat sheaf      101
Fourier — Sato transform      172
Full subcategory      24
Fully faithful      25
functor      24
Fundamental class      445
Generalized eigenspace      395
GENERIC      480
Germ (of a section)      84
Global homological dimension      77
Good filtration      446
Graded ring      447
Grothendieck group      77 399
Gysin map      179
Half-bicharacteristic curve      271
Hamiltonian isomorphism      258 478
Hamiltonian vector field      482 469
Heart      411
Hilbert syzygy theorem      443
Holomorphic differential operator      449
Holomorphic function      128
Holonomic ($\mathscr{D}$-module)      450
Homogeneous symplectic      482
Homological dimension (of a category)      75
Homotopic (cycles)      371
Homotopic (maps)      119
Homotopic (morphisms)      31
Homotopic (sheaves)      246
Hopf index theorem      408
Hyperbolic system      468
Image      28
ind-object      62
INDEX      361
Induced Cauchy — Riemann system      474
Inductive system      61
Inertia index      486
Infinite-order differential operators (ring of)      462
Initial object      24
Injective object      30
Injective subcategory (with respect to a functor)      50
Inverse Fourier — Sato transform      172
Inverse image (of a $\mathscr{D}$-module)      453
Inverse image (of a microfunction)      470
Inverse image (of a sheaf)      91
Involutive      271 478 481
Involutivity theorem      272
Isomorphism (of objects, of functors)      24
Isomorphism (on a subset of the cotangent bundle)      221
Isotropic      478
Isotropic set (subanalytic, $\mathbb{C}$-analytic)      331 344
Kernel      27 164
Kuenneth formula      135
Lagrangian      478 481
Lagrangian chain      380
Lagrangian cycle      373
Lagrangian Grassmannian manifold      480
Lagrangian set (subanalytic, $\mathbb{C}$-analytic)      331 344
Laplace operator      469
Lefschetz fixed point formula      392
Lefschetz fixed point theorem      390
Legendre transformation (partial)      318
Leibniz formula      449
Leray acyclic theorem      125
Localization (of a category)      41
Locally cohomologically trivial      178
Locally conic ($\mathbb{R}^{+}$, $\mathbb{C}^{\times}$)      344 483
Locally constant sheaf      90
Mapping cone      34
Maslov index      487
Mayer — Vietoris sequence      115
Micro-hyperbolic system      468
Micro-support      221
Microdifferential operator      462
Microfocal Morse lemma      239
Microfocal operators (ring of)      462
Microlocal (proper) direct image      255
Microlocal Bertini — Sard theorem      332
Microlocal composition of kernels      294
Microlocal cut-off lemma (dual, refined)      225 252 253 254
Microlocal inverse image      255
Microlocalization      198
Microlocally composable      294
Middle perversity      426
Mittag-Leffler condition      64
Module (over a sheaf of rings)      87
monodromy      351
Monomorphism      24
Morphism      23
Morse function (with respect to an isotropic subset)      388
Morse inequalities      239
Multiplicative system      41
Nearby-cycle functor      350
Noetherian filtered ring      446
Noetherian sheaf      443
Non-characteristic      235 262
Non-characteristic ($\mathscr{D}$-module)      453
Non-characteristic deformation lemma      117
Non-characteristic for A on V      262
Normal bundle      185 481
Normal cone      187
Normal deformation      186
Null system      43
Object      23
Opposite category      24
Opposite ring      29
Order (in a filtered ring)      447
Orientation sheaf (relative)      126 153
Paracompact space      102
Perfect (complex of A-modules)      78
Perverse (sheaf)      427
Perversity      419
Poincare — Verdier duality      140
Poisson bracket      447 478 482
Polar set      170
Presentation (s-, finite free, free ...)      443
Presheaf      83
Principal symbol      449
Pro-object      62
Projective (system, limit)      61
Projective object      30
Propagation of singularities      468
Proper cone (in a vector bundle)      169
Proper map      103
Properly homotopic maps      119
Pure sheaf      312
Quantized contact transformation      465
Quasi-inverse      25
Quasi-isomorphism      40
Regular involutive      483
Relative cotangent bundle      238 241
Representable functor      25
Representative      25
Residue morphism      182
Ring (sheaf of)      87
S-acyclic (sheaf)      324
Sato hyperfunctions      127 130 466
Sato microfunctions      466
Schwartz distributions      127
Section (of a presheaf)      84
Sheaf      85
Shift (functor)      31
Shift (of a sheaf)      312
Shrinking space      395
Signature (of a quadratic form)      487
Simple sheaf      312
simplex      321
Simplicial complex      321
Singular support      467
Soft sheaf      132
Specialization      191
Splits (a sequence)      70
STACK      424
Stalk (of a presheaf)      84
Stratification      334
Stratum      334
Strictly exact      446
Subanalytic chain      366
Subanalytic cycle      369
Subanalytic set      327
Subcategory      24
Supple sheaf      132
Support (of a sheaf, of a section)      85 116
Symplectic form      477
Symplectic vector space      477
t-structure      411
Tangent bundle      481
Thick subcategory      49
Thom class      179
Topological submersion      151
Trace      79 361
Transversal (map)      190
triangle      35
Triangular inequalities      222
Triangulated category      38
Triangulation theorem      328
Truncated complex      33
Vanishing-cycle functor      351
var      352
Vertex      321
Vietoris — Begle theorem      121
Wave operator      469
Weak global dimension (of a ring or a sheaf of rings)      78 110
Weakly constructible ($\mathbb{R}$-, $\mathbb{C}$-, $\mathbb{S}$-)      322 339 347
Weierstrass division theorem      458
Whitney conditions ((a) and (b))      357
Yoneda's extension      81
Zariskian filtered ring      446
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