Guillemin V., Pollack A. — Differential topology :: Электронная библиотека попечительского совета мехмата МГУ

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Guillemin V., Pollack A. — Differential topology

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Название: Differential topology

Авторы: Guillemin V., Pollack A.

Аннотация:

This text fits any course with the word "Manifold" in the title. It is a graduate level book.

Язык:

Рубрика: Математика/Геометрия и топология/Алгебраическая и дифференциальная топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 221

Добавлена в каталог: 31.05.2006

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

Предметный указатель

Almost every      40
Alt operator      155
Alternating tensor      155
Antipodal map      38
Appropriate for intersection theory      107
Arcwise connected      38
Area form      170
Argument      188
Argument principle      151
Ball in $\mathbf{R}^k$       5
Borsuk — Ulam theorem      91
Boundary definition      57
Boundary of homotopy space $X \times I$       99
Boundary orientation      97
Boundary theorem      80
Brouwer fixed-point theorem      65
Brouwer theorem of fixed point      65
Canonical immersion      14
Canonical submersion      20
Cartesian product      4
Cauchy integral formula      192
Cauchy — Riemann equation      192
Chain rule      8 11
Change in $\mathbf{R}^k$       166
Change of variables      165
Change on manifolds      168
Classical Stokes theorem      152
Classification of one-manifolds      64 208
Classification of two-manifolds      124
Closed curve      172
Closed form      178
Cobordant      84 187
Cocycle condition      174
Codimension      24
Cohomologous forms      179
Cohomology class      179
Cohomology group      179
Commutative      9
Compact support      (see Compactly supported form)
Compactly supported form      166
Compactly supported isotopy      142
Complementary dimension      77
Complementary dimensions      77
Complex valued form      192
Contractible      38
Coordinate function      4
Coordinate system      3
Critical point      40
Critical value      21
Cross section      55
Curl      178
Curvature of hypersurfaces in $\mathbf{R}^k$       195
Curvature of one-manifolds in $\mathbf{R}^2$       75
Curve      12
De Rham cohomology group      179
Deformation      38
Degree and integration      (see Degree formula)
Degree formula      188
Derivative map of tangent bundles      50
Derivative of forms      (see Exterior derivative)
Derivative of maps of Euclidean spaces      8
Derivative of maps of manifolds      10
Determinant tensor      153
Determinant theorem      160
Diagonal      7
Diffeomorphism      3
Differential of a function      163
Differential of forms      (see Exterior derivative)
DIMENSION      3
Direct sum orientation      100
Divergence      178
Divergence theorem      152
Embedding      17
Epsilon neighborhood      69
Epsilon neighborhood theorem      69
Equivalent maps      14
Equivalently oriented bases      95
Euler characteristic      116 148
Even permutation      155
Exact form      178
Exact sequence      103
Extension theorem for maps into spheres      145
Extension theorem for transversal maps      72
Exterior algebra      159
Exterior derivative in $\mathbf{R}^k$       174
Exterior derivative on manifolds      176
Fixed point      33
Flow      134
FORM      162
Fubini theorem      204
Fundamental theorem of algebra      82 110
Gauss map      195
Gauss — Bonnet theorem      196
General position      74
Generalized Stokes theorem      183
Genus      124
Global Lefschetz number      19
Global property      3
Gradient field      140 177
Graph      7
Green's theorem      152
Half space      57 63
Hessian matrix      41
Holomorphic function      192
Homotopy      33
Homotopy class      34
Hopf degree theorem      146
Hypersurface      86 195 219
Immersion      14
Independent functions      23
INDEX      133
Integral of forms on $\mathbf{R}^k$       166
Integral of forms on manifolds      167
Integral of forms on submanifolds      168
Integral of functions      195
Interior      57
Intersection, transversal      30
Inverse function theorem      13 19 56
Inward unit normal vector      63
Isotopy      142
Isotopy lemma      142
Jacobian      195
Jacobian matrix      8
Jordan curve theorem      85
Jordan — Brouwer separation theorem      89
Klein bottle      48 49
Lefschetz fixed point      33 120
Lefschetz map      33 120
Lie group      23
Line integral      169 172
Linear coordinate system      6
Linear coordinates      6
Linear orientation preserving map of vector spaces      96
Local computation Lefschetz number      130
Local diffeomorphism      13 14
Local immersion theorem      15
Local Lefschetz number      121 127
Local property      2
Local submersion theorem      20
Locally finite cover      56

Manifold      3
Manifold product      4 58
Manifold with boundary      57
Map product      7
Mayer — Vietoris argument      181
Measure zero      39 202
Mobius band      63
Mod 2 degree      80
Mod 2 intersection number of map and submanifold      78
Mod 2 intersection number of two maps      83
Mod 2 intersection number of two submanifolds      79
Mod 2 self-intersection      79
Mod 2 self-intersection number      79
Morse function      43
Morse lemma      42
Multilinear      153
Multiplicity      110
Negatively oriented bases      95
Negatively oriented basis      95
Nondegenerate critical point      41
Nondegenerate zero      139
Nonretraction theorem      65
Normal bundle      71
Normal bundle of diagonal      76
Normal bundle of submanifold (relative)      76
Normal space      71
Normal vector field      106
Normal vector inward      63 98
Normal vector outward      64 98
Odd permutation      155
One-dimensional manifold      64 208
One-manifolds classification      64 208
Open ball      5
Opposite orientation      97
Orientable manifold      96
Orientation for manifolds      96
Orientation for vector spaces      95
Orientation number (for zero-dimensional spaces)      96
Orientation of boundary      97
Orientation preimage      100
Orientation preserving map of oriented manifolds      96
Oriented degree      105
Oriented intersection number of map and submanifold      107
Oriented intersection number of two maps      113
Oriented intersection number of two submanifolds      112
Oriented manifold      97
Oriented self-intersection      115
Oriented self-intersection number      115
Orthogonal group      22
Orthonormal basis      161
Parametrization      3 57
Partition of unity      52
Permutation group      155
Poincare lemma      181
Poincare — Hopf index theorem      134
Positively oriented bases      95
Positively oriented basis      95
Preimage      21
Preimage orientation      100
Preimage theorem      21
PRODUCT      58
Product orientation      97
Projection map      55 71
Proper map      17
Pull-back form      163
Pullback cohomology classes      179
Pullback forms      163
Pullback vector fields      134
Rectangular solid      202
Regular point      40
Regular value      21
Relative normal bundle      76
Relatively open      2
Restriction form      168
Restriction of forms      168
Retraction      65
Saddle point      123
Sard's theorem      39 62 205
Second fundamental theorem of calculus      152
Short exact sequence      103
Sign of a basis      95
Simply connected      38
Sink      123
Smooth family of maps      39
Smooth form      165
Smooth map      1 2
Source      122
Sphere      4
Sphere bundle      55
Splitting proposition      126
Stability theorem      35
Stable class      34
Stable property      34
Stack of records theorem      26 81
Stereographic projection      6
Submanifold      5
Submersion      20
Support form      166
Support of a form      166 221
Tangency to a vector field      134
Tangent bundle      50
Tangent space      9
Tangent space of boundary      60
Tangent space of diagonal      12 76
Tangent space of graph      12
Tangent space of intersection      32
Tangent space of manifold with boundary      59
Tangent space of preimage      33
Tangent space of product      12
Tangent space preimage      33
Tangent to vector      9
Tangent to vector field      134
Tangent vector      9
Tensor      153
Tensor alternating      155
Tensor determinant      153
Tensor product      154
Torus      6
Transpose map      159
Transversal intersection      30
Transversal map      28 72
Transversaliry theorem      68
Transversality homotopy theorem      70
Triangulation      148
Trivial normal bundle      76
Tubular neighborhood      76
Tubular neighborhood theorem      76
Two-dimensional manifold      124
Unit normal      (see Normal vector)
Upper half space      57 63
Urysohn theorem      56
Vector field      55 132
Vector field gradient      177
Velocity vector      12
Volume      194
Volume element      161
Volume form on a manifold      194
Volume form on Euclidean space      164
Wedge product      156 162
Whitney embedding theorem      48
Whitney immersion theorem      55

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