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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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90 39 459 425 441 148 373 51 462 404 440 90 90 385 384 91 408 270 327 358—359 359—360 335—336 506 506 505 519 505 505 505 379 379 Abelian 40 Abelian 35 Absolute 401 Absolute 148 Absolute homology group 172 175 Absolute Hurewicz isomorphism theorem 397—398 Absolute Hurewicz isomorphism theorem, generalization of 508—509 Absolute neighborhood retract 56 Absolute neighborhood retract, tautness of 290—291 Absolute retract 56 Action of the fundamental group 382—385 420 Acyclic chain complex 163 Additive cohomology operation 270 Adem relations 276 Adjoint functor 41 Adjunction space 56 Admissible lifting 476 Admissible map 476 Affine variety 10 Affinely independent set 10 Alexander cohomology 308 Alexander cohomology, universal-coefficient formula 336 Alexander cohomology, universal-coefficient formula, for compact supports 337—338 Alexander cohomology, with compact supports 320 Alexander duality theorem 296 Alexander — Spanier cohomology see Alexander cohomology Alexander — Whitney diagonal approximation 250 Associated graded module 468 Associative coproduct 266 Associative product 263 Attaching map 146 Augmentation 167 213 Augmentation, of cochain complex 237 Augmentation-preserving chain map 168 Augmented chain complex 167 213 Augmented cochain complex 237 Axiom of compact supports 203 Axioms, of cohomology theory 240—241 Axioms, of cohomology theory, of homology theory 199—200 Back 250 Ball 9 Bary center 117 Barycentric coordinate 111 Barycentric subdivision 123—124 Barycentric subdivision, interation of 124 Base of cone 116 Base point 15 Base point, nondegeneracy of 380 419 Base space 62 66 90 Base vertex 110 136 Basis 6 8 Betti number 172 176 Bidegree 466 Bigraded module 466 Bijection 2 Bijective function 2 Binormal space 56 Block dissection 277 Bockstein cohomology homomorphism 240 Bockstein cohomology operation 270 Bockstein homology homomorphism 222 Bockstein homomorphism 280—281 Borsuk Homotopy Extension Theorem 57 Borsuk — Ulam theorem 104 266 Boundary 157 Boundary operator 156 Boundary, of homology manifold 277 Boundary, of pseudomanifold 150 Bounded subset 319 Brouwer degree theorem 398 Brouwer fixed-point theorem 151 194 Brouwer theorem on invariance of domain 199 Brown representability theorem 411 Bundle projection 90 Canonical free resolution 219 Canonical map 152 Canonical projection 152 Cap product 254—255 Carrier 112 Cartan formula 271 Category 14 Category, of a topological space 279 Category, of chain complexes 158 Category, of connected covering spaces 79 Category, of contiguity classes 130 Category, of fibrations 69—70 Category, of maps 414 Category, of morphisms 16 Category, of pairs 16 Category, of simplicial pairs 10 Category, opposite 17 Category, small 14 Category, with models 164 Cellular homotopy 403—404 Cellular map 403 Cellular-approximation theorem 404 Chain 157 Chain complex 157 Chain complex, acyclicity of 163 Chain complex, chain contractibility of 163 Chain complex, modulo 519 Chain complex, over a ring 213 Chain contraction 163 Chain equivalence 163 192 Chain homotopy 162 Chain homotopy class 205 Chain map 158 Chain transformation 158 Characteristic class 261 281 Characteristic map 91 457 Characteristic map, for a cell 146 Classification theorems 427 431 451 452 460 Classifying space 408 Closed edge path 135 Closed path 46 Closed simplex 111 Clutching function 102 455 Coboundary 236 Coboundary operator 236 Cobounded subset 319 Cochain complex 236 Cochain homotopy 236 Cochain map 236 Cocycle 236 Coexact sequence 366 418 Cofibered sum 99 Cofibration 29 33 57 Cofibration, induced 99 (see also Homotopy extension property) Coherent topology 5 Coherent topology, for simplicial complex 111 Cohomology algebra 264 Cohomology algebra, of projective space 264—265 Cohomology extension of fiber 256 Cohomology functor 407 Cohomology module 236 Cohomology module, with coefficients 237 Cohomology operation 269 429—430 Cohomology operation, additivity of 270 Cohomology operation, induced by coefficient homomorphism 270 Cohomology operation, of Bockstein 270 Cohomology operation, suspension of 431 Cohomology theory 240 Cohomology, K 247—249 Cohomology, of a group 502—503 Cohomology, universal-coefficient formula 243 246 283 Cohomology, with local coefficients 282—283 Cohomotopy group 421 461 Collaring 297 Comb space 26 Commutative coproduct 266 Commutative diagram 16 Commutative product 263 Compact pair 203 Compact supports 203 Compact-open topology 5 Compactiy generated space 5 Compatible family, in a presheaf 324 Compatible family, of cohomology classes 261 Compatible family, of homology classes 299 Compatible family, of orientations 207 Complementary degree 468 Completion of presheaf 325 Component, of groupoid 45 Component, of simplicial complex 138 Composite, of functions 2 Composite, of morphisms 14 Comultiplication 39 Comultiplication, homotopy associativity of 39 Comultiplication, homotopy identity for 39 Comultiplication, homotopy inverse of 40 Cone 56 116 Conjugacy class 15 Connected groupoid 45 Connected Hopf algebra 267 Connected simplicial complex 138 Connecting homomorphism 182 213 222 236 240 Constant presheaf 323 Contiguity category 130 Contiguity class 130 Contiguous simplicial maps 130 Continuity property 319 358 Contractible space 25 56 Contraction 25 Contravariant functor 18 Convergent factorization 438 Convergent filtration 468 493 Convergent sequence of fibrations 438 Convergent spectral sequence 467 Convex body 10 Convex set 10 Coordinate neighborhood 292 Coproduct 266 Counit 266 Covariant functor 18 Covering projection 62 Covering projection, induced 98 Covering space 62 103 Covering space, of projective space 80 Covering space, of sphere 80 103 Covering space, of topological group 104 Covering transformation 85 Cross product 231—232 234—235 Cross product, in cohomology 249—250 Crosscap 148—149 cube 9 Cup product 251—253 CW$ approximation 412 420 CW$ complex 401 420 CYCLE 157 Cyclic module 9 Deformable subspace 29 Deformation 29 Deformation retract 30 Deformation retraction 30 Degree 157 Degree, of homomorphism 157 Degree, of map 54 196 207 DG$ group 157 Diagonal approximation 250 Diagonal approximation, of Alexander — Whitney 250 Diagram chasing 186 Diagram, commutativity of 16 Diagram, homotopy commutativity of 25 Difference between two liftings 434 Differential 156 Differential graded group 157 Differential group 156 Dimension axiom 200 Dimension axiom, for cohomology 240 Dimension, of CW complex 401 Dimension, of simplex 108 Dimension, of simplicial complex 109 Dimension, of topological space 152 Dimension, theory of 152 Direct limit 3 Direct limit, of chain complexes 162 Direct limit, of direct system 18 Direct system 3 Direct system, in a category 18 Directed set 3 Discontinuous group 87 Dissection 276—277 Dominated space 421 Double suspension 516—517 Duality in suspension category 463 Duality map 462 Duality theorems, for manifolds 296 351 357 Duality theorems, in suspension category 463 Duality theorems, of Alexander 296 Duality theorems, of Lefschetz 278 297—298 Duality theorems, of Poincar 296—297 Duality theorems, of Whitney 281 355 EDGE 134 Edge path 134 Edge path group 136 151 208 Edge path group, of graph 140—141 Edge path groupoid 136 Edge, end of 134 Edge, origin of 134 Eilenberg — MacLane space 424 Eilenberg — Zilber theorem 232—234 Endomorphism, trace of 9 Epimorphism 6 Equalizer 406 EQUIVALENCE 15 Equivalence class 2 Equivalence relation 2 Equivalence, in homotopy 25 Equivalence, naturality of 22 Equivalence, of edge paths 135 Equivalence, of fiber bundles 92
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structure 
cogroup 
-stem 
-characteristie cohomology class 
th-power cohomology operation 
ech cohomology 
nneth formula 
-acyclic pair 
-homotopic maps 
complex 
-face 
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