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Dold A. — Lectures on Algebraic Topology
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: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Mayer — Vietoris-sequence of a pair of excisive triads      52
Models, acyclic      174
Module      124
Module over a graded ring      195
Mono-functor      130
Monomorphic      7
Morphism      2
Morphism functor      4
Morphism in a graded abelian group      195
Morphism in a space      193
Multiplicative properties of the transfer      314
Multiplicity of a counterimage      68
Natural diagonal      178 183 185
Natural equivalence      4
Natural transformation      4
Neighborhood retract      36
Nerve of a covering      355
Nerve of a family of subsets      119
Non-orientable surface of genus $k$      100
Normal Euler class      316
Nullhomotopic      14
nullhomotopy      14
Numerable covering      355
Numeration functor      356 360
Numeration of a covering      355
Object      1
Operation (of an $H$-space)      196
Opposite category      2
Opposite ring      124
Order linearly related      112
Ordered simplicial atlas      112
Ordered simplicial map      115
Ordered vertex schema      119
Orientable      271
Orientable along $A$      254
Orientable surface of genus $g$      59 99
Orientation at $P$      252
Orientation bundle      253
Orientation covering      255
Orientation manifold      255
Orientation of a map $M’\rightarrow M$      271
Orientation of cells      109
Orientation preserving      70 200 259 268
Orientation reversing      70 200 268
Over $A$, polyhedron      367
Pair of spaces      15
Partition of unity      354
Pass to the limit      275 349
Passage to quotients      125
Passage to the limit      275 349
Poincar$\acute{e}$ dual      292
Poincar$\acute{e}$ duality      298
Poincar$\acute{e}$ — Lefschetz duality      291 300
Poincare duality      298
Point-finite      354
Pointed space      45
Polyhedron under $A$      352
Polynomial algebra      231
Pontrjagin product      194
Pontrjagin ring      196
Pontrjagin slant product      246
Pro-free      177
PRODUCT      6
Product category      3
Product of pairs      15
Product orientation      256
Projection onto the factors      6
Projective functor      177
Projective module      149
Projective space      97 102
Projective space $P_{n}\mathbb{R}$      110
Proper map      70 268
Quasi-ordering      272
Quotient module      125
Range of a morphism      2
Rank of an abelian group      12 13
Reduced homology      34 153
Reduced homology sequence      34 153
Reduced Mayer — Vietoris-sequence      50
Relative $CW$ space      95
Representable functor      6
Resolution      132
retract      36
Retraction      36
Right exact functor      130
Right inverse      3
Scalar product      187
Scalar product of the orientation bundle      253
Scalar product with bounded support      260
Scalar product with compact support      266
Scalar product with respect to a pairing      188
Separates, $X_{1}\cap X_{2}$$X_{1}, X_{2}$      284
Short complex      27
Short exact      7
Shuffle      184
Shuffle map      184
Sign rule      162
Signature      304
Signature of $M$      305
Simplex of a simplicial space      113
Simplicial approximation      119
Simplicial atlas      111
Simplicial complex      120
Simplicial complex of a pair      120
Simplicial homology      121
Simplicial map      115
Simplicial space      112
Simplicial structure      112
Simplicial subspace      113
Singular chain      30
Singular chain with coefficients in $G$      150
Singular cochain with coefficients in $G$      150
Singular cohomology      150 151
Singular complex      31
Singular homology      32 150
Singular simplex      30
Skeleton, $m$      88 89
Small category      177
Smooth manifold      251
Split algebra      228
Split exact sequence      8
Stability      191 216 218 220 239
Stack numeration      357
Stacked covering      357 361
Stacking function      357
Standard maps between cells and spheres      54
Star, open star of a vertex      119
Stiefel manifold      329
Stiefel — Whitney class      335
Strong deformation retract      39
Strong topology      116 354
Strongly additive functor      128
Strongly cofinal      349
Stunted projective space      98
Sub category      3
Sub module      125
Subcategory      3
Suspension of a complex      18
Suspension of a space      51
Tensor product      142 161 221 222
Tensor product of complexes      161
Tensor product of graded algebras      221 222
Thom class      316
Thom Isomorphism      297 321
Topological group      196
Topological sum      6
Torsion coefficients      12 27
Torsion free      144
Torsion product      142 162
Torsion product of complexes      162
Torsion subgroup      12
Trace      208
Transformation of direct (inverse) systems      272
Transversally, intersect      317
Transverse class      315 323
TREE      103
Triad      15
Triangulation      112
Triple of spaces      15
Under $A$, polyhedron      352
Universal coefficient sequence      137 139 153
Universal coefficient theorem      137 138
Universal element      5
Universal property      5
Universal property of a base      11
Universal property of the Kan ($\check{C}$ech) extension      365
Universal transformation      273 348
Vector field, tangent      66
Vertex of a simplicial space      113
Vertex schema      116
Weak continuity of $\check{C}$ech-extensions      367
Weak topology      89 112
Weakly cofinal      349
wedge      45 46
Winding number      77 202
Yoneda-lemma      5
1 2
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