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

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Lavendhomme R. — Basic Concepts of Synthetic Differential Geometry
Lavendhomme R. — Basic Concepts of Synthetic Differential Geometry

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Basic Concepts of Synthetic Differential Geometry

Автор: Lavendhomme R.

Аннотация:

Starting at an introductory level, the book leads rapidly to important and often new results in synthetic differential geometry. From rudimentary analysis the book moves to such important results as: a new proof of De Rham's theorem; the synthetic view of global action, going as far as the Weil characteristic homomorphism; the systematic account of structured Lie objects, such as Riemannian, symplectic, or Poisson Lie objects; the view of global Lie algebras as Lie algebras of a Lie group in the synthetic sense; and lastly the synthetic construction of symplectic structure on the cotangent bundle in general. Thus while the book is limited to a naive point of view developing synthetic differential geometry as a theory in itself, the author nevertheless treats somewhat advanced topics, which are classic in classical differential geometry but new in the synthetic context. Audience: The book is suitable as an introduction to synthetic differential geometry for students as well as more qualified mathematicians.


Язык: en

Рубрика: Математика/Геометрия и топология/Дифференциальная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 320

Добавлена в каталог: 19.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$\mathcal C^\infty$-algebra      305
Abstraction symbol      270
Action of a Lie group      248
Action of a Lie object      191
Adjoint of a left action      250
Adjoint representation      252
Affine automorphism      246
Affine vector field      246
Almost complex connection      229
Almost complex structure      226
Almost Hermitian object      230
Arc of marked surface      117
Axiom, Bunge      59
Axiom, Fermat — Reyes      26
Axiom, general Kock      42
Axiom, integration      19
Axiom, Kock — Lawvere      2
Axiom, Koszul      182
Axiom, Lie-module      182
Axiom, preorder      17
Axiom, Wraith      58
Based vector field      254
Bianchi identity      200
Boundary operator      108
Breadth of a Weil algebra      36
Bunge axiom      59
Category      279
Characteristic function      295
Classical differential form      104
Classical global differential form      184
Coadjoint representation      253
Coequalizer      283
Complex object      227
Connecting map      257
Connecting mapping      163
Connection      143
Connection form      163
Connection on a vector bundle      255
Connection, almost complex      229
Connection, global      145
Connection, linear      192
Connection, pointwise      143
Connection, Riemannian      212
Connection, symmetric      155
Contravariant functor      281
Coproduct      283
Covariant derivation      147
Covariant derivation on a vector bundle      257
Covariant differential      169
Curvature      176
Curvature form      174
De Rham cohomology      116
Degenerate chain      136
Derivation      76
Derivation axiom      182
Derivative      6
Differential      12
Differential form      102
Differential form, classical      104
Differential form, classical global      184
Differential form, integral of a      110
Differential form, singular      102
Differential form, singular global      184
Diffusion      264
Diffusion on a vector bundle      264
Directional derivative      11
Distribution of dimension      99
Epimorphism      282
Equalizer      283
Euclidan vector bundle      66
Euclidean      5
Extensionality      278
Exterior differential      115
Exterior product      124
Fermat — Reyes axiom      26
Finite limit      50
Finitely complete      283
Formula      271
functor      280
General Kock axiom      42
Germ      309
Germ-determined ideal      309
Global connection      145
Global presymplectic structure      216
Global Riemannian structure      216
Good finite limit      52
h-antisymmetric      243
h-gradient      217
h-orthogonal      242
Hadamard's lemma      20
Hamilton equations      267
Hamilton operator      221
Hamiltonian      220
Height of a Weil algebra      36
Hermitian object      230
Hermitian structure      230
Holomorph      229
Homogeneous      15
Infinitesimal n-chain      108
Initial object      283
Integral of a differential forml      10
Integration axiom      19
Interior product      126
Isomorphism      282
Iterated tangent bundle      87
k-infinitesimally linear object      58
Kaelherian object      232
Killing vector field      244
Kock — Lawvere Axiom      2
Koszul's axiom      182
Left-invariant      240
Lie bracket      73
Lie derivative      76
Lie derivative in the direction of X      236
Lie derivative of a form      128
Lie group      239
Lie module axiom      182
Lie object      182
Lie operator      77
Lie R-algebra      73
Lie, action of a, group      248
Lie, action of a, object      191
Linear connection      192
Liouville 1-form      259
Liouville 2-form      259
Liouville's field      255
Localizing system      293
Locally Hamiltonian      220
Membership relation      270
Micro-square      87
Microcube      87
Microlinear      57
modus ponens      272
Monomorphism      282
Natural transformation      281
Object of line type      302
Operation symbol      270
p-form on a Lie object      187
Parallel transport      164
Pointwise connection      143
Pointwise pre-symplectic structure      216
Pointwise Riemannian structure      211
Poisson bracket      221
Poisson map      247
Poisson object      222
Poisson structure      223
Poisson tensor      224
Poisson vector field      247
Pre-symplectic structure      216
Pre-symplectic, global, structure      216
Predicate calculus      276
Preorder axiom      17
Presheaf      291
PRODUCT      283
Pullback      284
Quasi colimit      52
Reflexive immersed manifold      85
Reflexive object      81
Relation symbol      270
Relations are representable      287
Representable functor      282
Riemannian connection      212
Riemannian structure      211
Riemannian structure on a Lie object      212
Set of zeros of an ideal      309
Sheaf      291
Sheaf w.r. a localizing system      293
Singular differential form      102
Singular global differential form      184
Small object      36
Spectrum      33
Spray      151
Stokes formula      121
Strong difference      92
Subobject      284
Symmetric connection      155
Symplectic structure      220
Tensor product      123
Term      271
Terminal object      283
Theory of $\mathcal^\infty$-algebras      305
Topos      287
Torsion      171
Torsion form      170
Torsion of an almost complex object      226
Truth values object      278
Truth values object (in a topos)      295
TYPE      270
Variable      270
Varying set      287
Vector bundle      66
Vector field      69
Vector tangent      61
Weil algebra      35
Weil characteristic homomorphism      210
Weil, breadth of a Weil algebra      36
Weil, height of a Weil algebra      36
Well powered      284
Whitney sum      159
Wraith axiom      58
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте