Dold A. — Lectures on Algebraic Topology :: Электронная библиотека попечительского совета мехмата МГУ

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Dold A. — Lectures on Algebraic Topology

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Название: Lectures on Algebraic Topology

Автор: Dold A.

Аннотация:

Biography of Albrecht Dold Albrecht Dold was born on August 5, 1928 in Triberg (Black Forest), Germany. He studied mathematics and physics at the Univesity of Heidelberg, then worked for some years at the Institute for Advanced Study in Princeton, at Columbia University, New York and at the University of Zürich. In 1963 he returned to Heidelberg, where he has stayed since, declining several offers to attractive positions elsewhere. A. Dold's seminal work in algebraic topology has brought him international recognition beyond the world of mathematics itself. In particular, his work on fixed-point theory has made his a household name in economics, and his book "Lectures on Algebaic Topology" a standard reference among econimists as well as mathematicians.

Язык:

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

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1980

Количество страниц: 377

Добавлена в каталог: 16.04.2005

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Предметный указатель

decomposition      89
decomposition of mod       94
space      89
subspace      89
$C^{r}$ manifold      251
$C^{r}$ structure      251
$C^{s}$ submanifold      251
-space      280
-homology      150
$\check{C}$ ech cohomology      281
$\check{C}$ ech cohomology sequence      284
$\check{C}$ ech cohomology with bounded (compact) supports      288
$\check{C}$ ech extension      363
$\check{C}$ ech homology      122 340
$\mathbb{H}$ -map      194
$\mathbb{Z}_{p}$ characteristic      156
$\partial$ -manifold      249
$\partial$ -structure      173
(Co-)homology sequence      21 32 33 34 151 284
Absolute Mayer — Vietoris-sequence      48
Absolute neighborhood retract (ANR)      84
Action (of a group)      126
Acyclic      17
Acyclic model theorem      176
Acyclic models      174
Additive functor      127
Alexander duality      213 301
Alexander — Whitney map      184
Approximation, simplicial      119
Atlas      251
Attaching a collar to a $\partial$ -manifold      250
Attaching map      89
Augmentation      33 34
Barycentric coordinates      116
Barycentric subdivision      40 118
Base of a functor      174
Base of a module      125
Base of an abelian group      11
Base point      45
Biadditive,       158
Bilinear      161
Bockstein homomorphism      155
Boundary of $\Delta_{q}$       30
Boundary of a $\partial$ -manifold      249
Boundary of a chain      16
Bounded      172
Bounded from above      172
Bounded from below      172
Branch point      62
Brouwer fixed point theorem      57
Canonical base of a free complex      27
Cap product      238 288 293
Cap-product ( $\frown$ -product)      238 288 293
Carrier of a singular chain      198
Carrier simplex of a point      113
Category      1
Cell,       89
Cellular boundary homomorphism      106
Cellular chain map      106
Cellular complex      86
Cellular filtration      85
Cellular map      85
Cellular space      85
Chain      16
Chain homotopy      23
Chain map      16
Chain map of degree       167
Change of charts      251
Characteristic map      89
Chart      247 249
Chern class      333
Class of the graph      303
Classification, homotopy      169
Closure finiteness      89
Co product      6
Cobordism      306
Coboundary      151
Cocycle      151
Coefficient homomorphism      155
Coefficient sequence      155
Cofactors, injection of the      6
Cofinal      276 352
Cofunctor      3
Cohomology algebra      221
Cohomology of a complex      173
Cohomology operation      155
Cohomology ring      221
Cohomology slant product      234
Cohomology transfer      310
Coim ( $\alpha$ )      7
Coker ( $\alpha$ )      7
Collar, attaching a      250
Commutative (graded) algebra      195
Commutative graded ring      195
COMPLEX      16
Components of a homomorphism into a direct product      9
Components of a homomorphism of a direct sum      10
Components of an element in $\Pi$ $A_{\lambda}$       9
Composite morphism      2
Composition of morphisms      2
Cone construction      34
Connected algebra      227
Connecting homomorphism      20 32 136 151 283
Constant functor      4
Contiguous      359
Continuation of an orientation along a path      255
Continuity of $\check{C}$ ech cohomology      287
Contractible complex      24
Contractible space      38
Coordinate neighborhood      247 249
Coproduct      6
Cubical lattice      96
Cup product      219 288
Cup product of cochains      222
Cup-product ( $\smile$ -product)      219 288
Cup-product ( $\smile$ -product) of cochains      222
CYCLE      16
Decomposable      228
Deformation      13
Deformation retract      39
Degree of $\textit{f}$ over       267
Degree of $\textit{f}$ over a point      67
Degree of a map      62
Degree of a proper map      268
Derived (barycentric) coordinates      43
Derived barycentric coordinates      43
Derived functor      132
Derived transformation      132
Diagonal of an algebra      229
Diagonalclass      302
Diameter      46
Diffeomorphic      248
Dimension (of a -space)      89
Direct exact sequence of chain maps      22
Direct product      6 9
Direct product representation      10
Direct simplicial approximation      119
Direct sum      6 7 9
Direct sum of subgroups      10
Direct sum representation      10
Direct summand      11
Direct system      272
Directed category      352
Directed set      272
Distinguished subset      116
Divisible (module)      148
Divisible module      148
Domain (of morphism)      2
Dominated      353
Doubling (a ( $\partial$ -manifold)      250

Dual base      300
Dual Hopf algebra      233
Dual Hopf-algebras      233
Duality in $\partial$ -manifolds      301 303
Eilenberg — Zilber map      179 185
Eilenberg — Zilber theorem      179
Elementary (complex)      27
Elementary complex      27
Epi-functor      130
Epimorphic      7
EQUIVALENCE      3
Equivalence of categories      136
Euclidean neighborhood retract (ENR)      81 103
Euler class      316
Euler — Poincar $\acute{e}$ characteristic      104 105
Evaluation map      173 208
Exact functor      130
Exact homology sequence      21 32 33 34 151
Exact sequence      7
Excision      44 286
Excisive triad      47 286
Exterior algebra      231
Exterior cohomology product      215
Exterior homology product      190
Face of $\Delta_{q}$       30 96
Face of a simplex      112
Factors, projection onto the      6 9
Filtration of a space      85
Finite space      90
Finite type      172
Five lemma      8
Fixed point index      203 205 207
Flat module      144
Flat resolution      146
Free Abelian group      11
Free abelian group generated by A      11
Free commutative algebra      231
Free functor      174
Free module      125
Free part of       12
Full subcategory      3
functor      3
Fundamental class around       192 267
Fundamental cycle      57
Fundamental theorem of algebra      65
Generalized -manifold      259
Generalized manifold      259
Graded algebra      195
Graded group      17
Graded ring      195
Graph      95
Grassmann manifold      330
Group ring      126
Gysin sequence      326
H$-space      194
Half exact functor      130
Hereditary ring      126
Hom (of complexes)      167
Hom ${}_{R}$ (, )      124
Homogeneous coordinates      97
Homologous      16
Homology class      16
Homology group      16
Homology of a complex      16
Homology sequence      21
Homology sequence of a pair of spaces      32 151
Homology sequence of a triple of spaces      33
Homology slant product      246
Homology theorem      7
Homology transfer      310
Homomorphism -homology      124
Homothety      124
Homotopic      14 23
Homotopy      13 23
Homotopy associative      194
Homotopy category      15
Homotopy class      14 23
Homotopy classification      169
Homotopy commutative      194
Homotopy equivalence      15 24
Homotopy extension property (HEP)      84
Homotopy homomorphism      194
Homotopy invariance      14 37 361
Homotopy of degree       168
Homotopy rel.       14
Homotoy unit      194
Hopf algebra      229
Hopf invariant      225
Hopf map      97 225
Identity morphism      2
Im( $\alpha$ )      7
Improvement of $\pi$       354
Incidence number      109
Inclusion of the summand      9
Independent, topologically      248
Index, fixed point      203 205 207
Induced orientation      257
Injection of the cofactors      6
Injective module      148
Interior cohomology product      219
Interior homology product      193
Interior of a $\partial$ -manifold      249
Intersection class      336
Intersection multiplicity      325
Intersection number      197 344
Intersection pairing      197 336 341
Intersection product      336
Invariance of branch point order      62
Invariance of dimension      60
Invariance of domain      79
Invariance of simplicial homology      121
Invariance of the boundary      61
Inverse system      272
Isomorphism      3
Join of maps between spheres      66
Jordan theorem      78
K $\ddot{u}$ nneth relations for $\check{C}$ ech cohomology      301
K $\ddot{u}$ nneth sequence      164 168 181 182 190 215 222 301
K $\ddot{u}$ nneth theorem      164 168 181 182 190 215 222
Kan-extension      362 367
ker( $\alpha$ )      7
Lattice in $\mathbb{R}$       74 96
Lefschetz number      208
Lefschetz — Hopf fixed point theorem      209
Left exact functor      130
Left inverse      3
Lens space      100 101 111
Limit of a direct system      273
Limit of a functor      348
Linear map (into a simplicial space)      114
Linearly related      112
Linking number      202
Linking product      202
Local homology group      59 61
Local intersection number      198
Locally -connected      84
Locally closed      80
Locally finite      354
Locally flat sub manifold      249
Locally flat submanifold      249
Long line      250
Loop      196
Loop space      196
Manifold      247
Manifold with boundary (= $\partial$ -manifold)      249
Map of vertex schemata      116
Mapping cone      18 225
Maximal simplicial atlas      112
Mayer — Vietoris sequence      48 50 52 152 285
Mayer — Vietoris-sequence      152 285

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