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Spanier E.H. — Algebraic Topology
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Название: Algebraic TopologyАвтор: Spanier E.H. Аннотация: Intended for use both as a text and a reference, this book is an exposition of the fundamental ideas of algebraic topology. The first third of the book covers the fundamental group, its definition and its application in the study of covering spaces. The focus then turns to homology theory, including cohomology, cup products, cohomology operations, and topological manifolds. The remaining third of the book is devoted to Homotropy theory, covering basic facts about homotropy groups, applications to obstruction theory, and computations of homotropy groups of spheres. In the later parts, the main emphasis is on the application to geometry of the algebraic tools developed earlier.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1966Количество страниц: 542Добавлена в каталог: 16.07.2013Операции: Положить на полку |
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Euclidean space 9 Euler characteristic 172 205 Euler characteristic, of fibration 481—482 Euler class 347—348 Euler-Poincar see Euler characteristic Evaluation map 6 Evenly covered subset 62 Exact couple 472—473 Exact sequence 179 Exact sequence, of pointed pairs 366 461 Exactness axiom 200 Exactness axiom, for cohomology 240 Exactness theorem 182—183 Excision axiom 200 Excision axiom, for cohomology 240 Excision map 188 Excision property 188—189 Excisive couple 188—190 Exponential correspondence 6 Exponential law 6 Exponential map 53 Extended lifting function 93 Extension 2 Extension problem 20 28 Extension, of groups 179 Extension, of modules 242 Exterior algebra 264 Face, of simplex 108 Face, of singular simplex 160 Fiber 66 90 Fiber bundle 90 Fiber bundle, fibration property of 96 Fiber bundle, induced 98 Fiber bundle, triviality of 92 Fiber homotopy 99 Fiber homotopy equivalence 100 Fiber pair 256 Fiber space see Fibration Fiber-bundle pair 256 Fibered product 70 98 Fibration 66 104 Fibration, cohomology spectral sequence of 493—498 Fibration, homology spectral sequence of 480—481 Fibration, homotopy sequence of 377 Fibration, induced 98 Fibration, local 92 Fibration, with unique path lifting 68 Fibration, with unique path lifting, regularity of 74 Fibration, with unique path lifting, universality of 84 Filtered degree 468 Filtration 276 468 493 Filtration, bounded, above 493 Filtration, bounded, below 276 469 Filtration, convergence of 276 468 Filtration, of topological pair 472 Fine presheaf 330 Finite presentation 7 Finite simplicial complex 109 Finite type 246 Finitely generated graded group 172 First obstruction to lifting 446 First-quadrant spectral sequence 468 Five lemma 185—186 Five lemma, modulo 519 Fixed point 151 194—197 Fixed-point theorem, of Brouwer 151 194 Fixed-point theorem, of Lefschetz 195 Flow 197 Free approximation 225—226 Free basis 6 8 Free chain complex 157 Free functor 164 Free generating set 6 Free group 6 145 Free module 8 Free resolution 219 Freely homotopic maps 379 Front 250 Full subcategory 16 Full subcomplex 110 Fully normal space 316 functor 18—20 Functor, adjointness of 41 Functor, contravariance of 18 Functor, covariance of 18 Functor, of loop spaces 39 Functor, of several variables 22 Functor, of suspensions 41—42 Fundamental class 303 Fundamental family 301 Fundamental group 50 58—59 Fundamental group, action of 382—385 420 Fundamental group, of graph 141—143 Fundamental group, of lens space 88 Fundamental group, of orbit space 88 Fundamental group, of projective space 80 147 Fundamental group, of sphere 53 58 Fundamental group, of surface 149 Fundamental groupoid 48 Fundamental presheaf 326 Fundamental theorem of algebra 59 Generalized lens space 88 Graded algebra 263 Graded coalgebra 266 Graded group 157 Graph 139 Group, finite presentation of 7 Group, free generation of 6 Group, generators 6 Group, gradation of 157 Group, of homotopy classes 421 Group, relations 6 Group, without fixed points 87 Groupoid 45 Groupoid, component of 45 Groupoid, connectivity of 45 Gysin cohomology sequence 260 Gysin cohomology sequence, generalization of 499—500 Gysin homology sequence 260 Gysin homology sequence, generalization of 483 H$ cogroup, commutativity of 40 H$ cogroup, homomorphism of 40 H$ group 35 H$ group, commutativity of 35 H$ space 34 H$ space, homomorphism of 35 Handle 148 Height 264 Higher obstructions to lifting 446 Homogeneously 150 Homologically locally connected space 340 Homologous cycles 157 Homology class 157 Homology group 157 Homology group, of lens space 206 Homology group, of retract 193 Homology group, of simplex 171—174 Homology group, of sphere 190 Homology group, of surface 206 Homology manifold 277—278 Homology module 213 Homology module, of bigraded module 466 Homology operation 269 Homology sequence, of Mayer — Vietoris 187—190 Homology sequence, of pair 184—185 Homology sequence, of triple 184—185 201 Homology tangent bundle 294 Homology theory 199—200 208 Homology theory, with coefficients 218 Homology theory, with compact supports 203—205 Homology, K 228—232 Homology, of a group 503—504 Homology, of fiber bundles 258 279—280 Homology, universal-coefficient formula 222—226 248 282 Homology, with local coefficients 281—282 Homorphism, of 39 Homorphism, of 35 Homorphism, of homology theories 201 Homorphism, of presheaves 324 Homorphism, of sequences 180 Homorphism, of spectral sequences 467 Homotopy 23 Homotopy abelian 35 40 Homotopy axiom 200 Homotopy axiom, for cohomology 240 Homotopy category 25 Homotopy category, of maps 414 Homotopy category, of pairs 25 Homotopy category, of pointed topological spaces 25 Homotopy category, of topological spaces 25 Homotopy class 24 Homotopy class, of map pairs 414 Homotopy commutative diagram 25 Homotopy equivalence 25 Homotopy equivalence, of maps 414 Homotopy excision theorem 484—486 Homotopy extension property 28 57 118 Homotopy extension property, for polyhedral pairs 118 Homotopy extension theorem of Borsuk 57 Homotopy functor 407 Homotopy group 43—44 371 418—419 Homotopy group, finite generation of 509 Homotopy group, of spheres 398 459 520 Homotopy group, of spheres, 515—517 Homotopy group, of spheres, finiteness of 515—516 Homotopy identity 35 39 Homotopy inverse 25 35 40 Homotopy lifting property 66 (see also Fibration) Homotopy pair 414 Homotopy sequence, of pair 374 Homotopy sequence, of triple 378 Homotopy sequence, of weak fibration 377 Homotopy type 25 Homotopy, associativity 35 39 Homotopy, of paths 46 Homotopy, relative to a subspace 23 Hopf algebra 267 280 Hopf algebra, structure of 268 Hopf bundle 91 Hopf classification theorem 431 Hopf extension theorem 431 Hopf invariant 489—490 500—502 Hopf theorem on 269 Hopf trace formula 195 Hurewicz fiber space see Fibration Hurewicz homomorphism 388—390 Ideal of abelian groups 506 identity map 2 Identity morphism 14—15 Imbedding of projective spaces 356 361 Inclusion map 2 Index of manifold 357—358 Induced cofibration 99 Induced covering projection 98 Induced fiber bundle 98 Induced fibration 98 Induced homomorphism 158 Induced orientation of simplex 207 Induced subdivision 122 Induced weak fibration 375 Inessential map 23 Initial object 17 Injection 2 Injective function 2 Integral homology theory 218 interval 9 Invariance of domain 199 Inverse limit 3 Inverse limit, of chain complexes 162 Inverse limit, of inverse system 18 Inverse of morphism 15 Inverse system 3 Inverse system, in a category 18 Join of simplicial complexes 109 Jordan curve theorem 198 Jordan — Brouwer separation theorem 198 K 228—232 282 K 359—360 K 247—249 K 234—235 Kernel of induced map 365 Klein bottle 149 Lefschetz duality theorem 278 297—298 Lefschetz fixed-point theorem 195 Lefschetz number 194—195 Lens space 88 Lens space, generalization of 88 Leray structure theorem 268 Leray — Hirsch theorem 258 Lift see Lifting Lifting function 92 Lifting problem 65 Lifting theorem 76 Lifting, of map 66 Lifting, of map pair 415 Limit, direct 18 Limit, inverse 18 Line 10 Line segment 10 Linear metric 124 Linear singular simplex 176 Linking number 361 Local connectedness 103 Local fibration 92 Local homeomorphism 62 Local homomorphism 104 Local isomorphism 104 Local isomorphism, of presheaves 329 Local system 58 360 Locally constant function 309 Locally constant presheaf 360 Locally contractible space 57 Locally finite simplical complex 119 Locally isomorphic groups 104 Locally path-connected space 65 Locally zero cochain 307 Locally zero presheaf 328 Loop 46 Loop functor 39 Loop space 37 Manifold 292 356—357 Manifold, index of 357—358 Manifold, with boundary 297 Manifold, without boundary 292 Map pair 414 Map, degree of 54 196 207 Map, free homotopy of 379 Map, homotopy of 23 Map, lifted 66 Map, of pairs 22 Mapping cone 365 Mapping cone, of chain map 166 191 Mapping cylinder 32—33 Mapping cylinder, of pairs 33 Mapping path fibration 99 Mayer — Vietoris sequence 186—189 218 Mayer — Vietoris sequence, in cohomology 239 mesh 125 Mesh, of singular chain 177 Method of acyclic models 164—166 169
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