Greenberg M.J., Harper J.R. — Algebraic topology: a first course :: Электронная библиотека попечительского совета мехмата МГУ

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Greenberg M.J., Harper J.R. — Algebraic topology: a first course

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Название: Algebraic topology: a first course

Авторы: Greenberg M.J., Harper J.R.

Аннотация:

This book is intended as a first course, sufficiently comprehensive to enable the student either to use the subject in other fields of endeavor and/or to pursue its development and applications in more advanced texts and the literature.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 321

Добавлена в каталог: 04.12.2013

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

Предметный указатель

Absolute neighborhood retract      225
Acyclic      54
Acyclic carrier      200
Acyclic with augmentation      54
Adjoining a cell      112
Adjunction space      112
Affine map      42
Affine space      41
Alexander — Whitney homomorphism      251
Algebraic mapping cone      90
Antipodal map      95
Aspherical      55
Augmentation      54
Augmented homology, reduced homology      48
Backface      196
Ball      76
Barratt — Whitehead sequence      99
Barycenter      42
Barycentric coordinates      42
Betti numbers      128
Bockstein maps      192
Borsuk antipode theorem      127 229
Borsuk — Ulam theorem      223
Boundary      46 53
Bouquet-wedge      126
Brouwer fixed point theorem      19 84
Cap product      204
Cell (closed)      106
Cell complex (finite)      134
Cellular map      135
Chain      45
Chain complex      52
Chain equivalence      91 265
Chain homomorphism, chain map      52
Chain homotopy      33
Chain map      52
Characteristic map or cell complex      134
Closed form      178
Coalgebra      270
Cobordism      39 139 243
Coboundary      177
Cochain      174
Cocycle      177
Cohomology algebra      197
Cohomology module      177
Collaring, collared pair      112
Compact support (section)      166
Compact supports (cohomology)      215
Compact-open topology      32
Complex projective space      114
Cone      140
Connecting homomorphism      75
Continuation      158
Contractible      11
Contrafunctor      174
Convex      42
Covering space      21
Covering transformation      24
Cross product      259
Cup product      195 259
CYCLE      46 53
Deformation retract      82
Degeneracy operators      199
Degree (of a map)      85
Derivation      196
Derived functor (of $\otimes$ )      275
Derived functor (of hom.)      185
Dimension (in a complex)      52
Dimension (of a manifold)      28
Direct sum      47
Directed set      208
Double (of a manifold with boundary)      240
Dunce cap      146
Elienberg — Zilber theorem      252
Equivalence (of covering spaces)      27
Euler characteristic      128
Evaluation map      32
Evenly covered      21
Exact      54
Exact form      178
Exact homology sequence      75
Exact triad      98
Excision      82
Face      45
Fibres      21
final      211
Finite cell complex      134
Finite simplicial complex      136
Five lemma      77
Free functor      266
Front face      196
functor      3
Fundamental cohomology class      221
Fundamental group      9
Fundamental homology class      167
g-fold torus      67 123 191
Genus      124
Graph      101
H-space      33
Homogeneous      115
Homologous      47
Homology module      47 53
Homology sequence      75
Homotopy      7 11 73
Homotopy equivalence      13
Homotopy groups      34

Hopf invariant      204 207 274
Independent points      42
INDEX      243
Induced homomorphism      9 48 53
Inductive limit      209
Inside      109
Intersection number      291
Invariance of domain      110
Join      85
Join (of spaces)      104
Klein bottle      50 104 127 172
Knot      68 108
Kronecker product      179
Kuenneth exact sequence      255 262
Lefschetz fixed point theorem      286
Lefschetz number      285
Lens space      116 149 229 295
Lifting      26
Linking number      68
longitude      147
Loop      7
Manifold      28
Manifold with boundary      237
Mapping cone      141
Mayer — Vietoris sequence      99
Meridian      147
Models      266
Moebius band      69 171 173 237
Natural transformation      50
Naturality (=functionality)      49 77
Normal (covering space)      25
Normal extension      187
Orientable      161
Orientation (global)      160
Orientation (local)      160
Orientation sheaf      164
Orientation-preserving map      171
Outside      109
pair      71
Path      6
Poincare homology sphere      150
Pointed topological space      9
Polyhedron      136
Prism operator      62
Product orientation      287
Projective limit      210
Projective space      25 36 114 222 243 294
Proper map      215
Properly discontinuous      25
Quatemionic projective space      116
Rank      128
Reduced chain complex      54
Reduced homology      48
Relative boundary      71
Relative cohomology      179
Relative cup product      206 273
Relative cycle      71
Relative Eilenberg — Zilber theorem      273
Relative homeomorphism      113
Relative homology      70
Relative Mayer — Vietoris sequence      100 105
Representation of homology by submanifolds      292
Resolution (free)      184
retract      19 78
Retraction      4
Rose (r-leaved)      101
Section      164
Semi-locally simply connected      27
Sheets      21
Short exact sequence      79
Shuffle homomorphism      268
Simplex (geometric)      42
Simplex (singular)      44
Simplicial complex      136
Simplicial map      137
Simply connected      12
Skeleton      134
Skew-commutative      198
Slant product      263
Small of order $\mathscr{V}$       85
Spherical complex      114
Split exact sequence      79
Strong deformation retract      19
Subdivision      85
Support (of a chain)      106
Surgery      151
Suspension      126
Suspension isomorphism      93 126
Tautly imbedded      230
Thom class      277 295
Thom isomorphism theorem      282
Topologist’s sine curve      55 127 182
Torus      18 50 68 102 146 147 172
TRANSPOSE      176
Transverse class      295
Transverse intersection      290
Triad      98
Triangulation      136
Triple      77
Truncated polynomial algebra      223
Twist      147
Universal coefficient theorem      189 256
Universal covering space      27
Vector field (on a sphere)      95
Vertex of cone      140
Weak homotopy equivalence      137
Wedge (=bouquet)      126

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