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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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Metric topology of simplical complex 111 Model 164 Module, of extensions 241—242 278—279 Module, of homomorphisms 8 238—239 Module, rank of 8 Module, structure theorem 9 Monomorphism 6 Moore — Postnikov factorization 440 Moore — Postnikov sequence of fibrations 440 Moore — Postnikov tower 440 Morphism 14 Morphism, composite of 14 Morphism, identity 14—15 Morphism, inverse of 15 Multiplication 34 Multiplication, homotopy abelian 35 Multiplication, homotopy associativity of 35 Multiplication, homotopy identity for 35 Multiplication, homotopy inverse for 35 Multiplicity 73 Natural equivalence 22 Natural transformation 21 Nerve 109 152 Noether Isomorphism Theorem 7 Nondegenerate base point 380 419 Nonnegative chain complex 157 Nonorientable pseudomanifold 206—207 Normal Stiefel — Whitney classes 354 Null homotopic map 23 Number of sheets 73 Numerable covering 93 Object 14 Object, initial 17 Object, terminal 17 Obstruction to lifting 433 Open covering of pair 311 Open simplex 112 Opposite category 17 Orbit 87 Ordered chain complex 170 Orientable fibration 476 Orientable homology manifold 278 Orientable manifold 294—297 Orientable pseudomanifold 206—207 Orientable sphere bundle 259 Orientation class 259 Orientation presheaf 326 Orientation, of manifold 294—297 Orientation, of pseudomanifold 207 Oriented chain complex 159 Oriented cohomology 238 Oriented homology functor 160 Oriented homology group 159 Oriented homology group, with coefficients 214 Oriented pseudomanifold 207 Oriented simplex 158 Oriented sphere bundle 259 Origin of edge 134 Pair, homology sequence of 184—185 Pair, homotopy sequence of 374 Pair, of spaces 22 Pair, tautness of 289 Pairing, of modules 250 Pairing, of spectral sequences 491 Partial order 2 Partially ordered set 2 Path 46 Path class 46 Path class, category of 48 Path component 48 Path connected 48 Path space 75 99 Path, closedness of 46 Path, end of 46 Path, origin of 46 Path, product of 46 Poincare duality theorem 296—297 Pointed pair, exact sequence of 366 461 Pointed set 15 Pointed simplical complex 110 Pointed topological space 15 Polar coordinates in a simplex 117 Polyhedral pair 114 Polyhedron 113 149—150 Polynomial algebra 264 Postnikov factorization 440 Postnikov sequence 440 Presentation of group 6 Presheaf 323 Presheaf, fineness of 330 Principal fibration 432 Principal fibration, of type ( 433 Principal simplex 208 PRODUCT 263 Product bundle 90 Product, fibered 70 98 Product, in category 17 Product, of categories 17 Product, of chain complexes 161 Product, of edge paths 135 Product, of pairs 234 Product, of paths 46 Product, of sets 2 Product, topological 4 Product-bundle pair 256 Projection chain map 158 Projection map 3 Projective space 9 146—147 Projective space, cohomology algebra of 264—265 Projective space, covering space of 80 Projective space, fundamental group of 80 147 Projective space, imbedding of 356 361 Proper face 108 Proper map 319 Properly discontinuous group 87 Pseudomanifold 148 150 206—208 Pseudomanifold, without boundary 148 Quotient chain complex 158 Quotient set 3 Quotient space 5 Rank of module 8 Realization 120 Reduced chain complex 168 Reduced cochain complex 237 Reduced cone 365 Reduced homology group 168 200 Reduced homology sequence 184—185 Reduced Mayer — Vietoris sequence 187—189 Reduced squares 270—271 Reduced suspension 41 Regular fibration 74 Relative 412 Relative 401 420 Relative Alexander presheaf 323 Relative homeomorphism 202 Relative homology group 172 175 Relative homotopy group 372 Relative homotopy of liftings 415 Relative Hurewicz isomorphism theorem 397 Relative Hurewicz isomorphism theorem, generalization of 511 Relative lifting problem 415 Relative manifold 297 Relative Mayer — Vietoris sequence 187—190 Relative singular presheaf 324 Resolution 219 Restriction 2 Restriction, in presheaf 323 retract 28 Retract, absolute 56 Retract, absolute neighborhood 56 Retract, deformation 30 Retract, deformation, strong 30 Retract, deformation, strong, of pairs 33 Retract, deformation, weak 30 Retract, weak 28 Retracting function 97 Retraction 28 Retraction, deformation 30 Retraction, deformation, strong 30 Retraction, weak 28 Ring of abelian groups 506 Section 77 Self-equivalence of fibration 85 Semilocally 1—connected space 78 Serre class of abelian groups 504 Serre cohomology sequence 519 Serre fibre space see Weak fibration Serre homology sequence 519 Sheaf 324—325 360 Short exact sequence 179 Short exact sequence, of chain complexes 180 Shrinking of an open covering 331 Simple map 440 Simple order 2 simplex 108 Simplical approximation 126—128 Simplical complex 108 Simplical complex, finer than covering 124 Simplical complex, homogeneously n-dimensional 150 Simplical map 109 150—151 Simplical mapping cylinder 151 Simplical pair 110 Simplical product 359 Simplical-approximation theorem 128 Singular chain complex 161 Singular cohomology 238—239 Singular cohomology, with compact supports 323 Singular cohomology, with local coefficients 282—283 Singular homology functor 161 Singular homology group 161 Singular homology group, K 234—235 Singular homology group, with coefficients 214 Singular homology group, with local coefficients 281—282 Singular simplex 160 Six-term exact sequence 224 278—279 Skeleton 109 Skeleton, of relative 401 Slant product 287 351 Small cell 299 Solenoid 358 Space, compactly generated 5 Space, obtained by adjoining cells 145 Space, of adjunction 56 Space, of loops 37 Space, of orbits 87 Space, of paths 75 Space, of simplical complex 111 Space, of type ( 424 460 Spanier — Whitehead duality theorem 463 Spectral sequence 466 Spectral sequence, convergence of 467 Spectral sequence, in suspension category 518 Spectral sequence, of fibration 480—481 493—498 Spectral sequence, of filtered chain complex 469 Sperner Lemma 151 Sphere 9 Sphere, fundamental group of 53 58 Sphere, homology of 190 Sphere, homotopy groups of 398 459 515—520 Split short exact sequence 216 Standard Postnikov factorization 446 Star 114 Star refinement 316 Starlike subset 53 Steenrod algebra modulo 2 276 Steenrod classification theorem 460 Steenrod squares 270—271 stem 459 Stiefel — Whitney characteristic classes 281 Stiefel — Whitney characteristic classes, of manifold 349 Strong deformation retract 30—33 Strong deformation retraction 30 Strong excision property 317—318 Strongly single space 510 Structure group 90 Structure, of finitely generated module 9 Structure, of Hopf algebra 268 Subcategory 16 Subcategory, fullness of 16 Subcomplex, of chain complex 158 Subcomplex, of relative 402 Subcomplex, of simplical complex 110 Subdivision 121 Subdivision chain map 192 Subdivision, induced 122 Subdivision, of singular chains 178 Subpair 22 Sum, cofibered 99 Sum, in category 17 Sum, of chain complexes 161 Sum, of sets 2 surface 148 Surface, fundamental group of 149 Surface, homology of 206 Surjection 2 Surjeetive function 2 Suspension 41 461—462 Suspension category 462—463 Suspension functor 41—42 Suspension theorem 458 Suspension, of cohomology operation 431 Suspension, reduced 41 Tangent bundle 91 Taut pair 289 Tautly imbedded pair 289 Tautness, for absolute neighborhood retracts 290—291 Tautness, of Alexander cohomology theory 316—317 Tensor product 7 213—217 Tensor product, of chain complexes 228 Tensor product, of presheaves 324 Terminal object 17 Thom class of sphere bundle 283 Thom isomorphism theorem 259 Thom — Gysin sequence 260 (see also Gysin cohomology sequence; Gysin homology sequence) Topological pair 22 Topological sum 5 Topology, coherent with collection 5 Topology, coinduced 4 Topology, induced 4 Torsion coefficient 172 176 Torsion product 219—221 224—225 278-279 Torsion product, of chain complexes 228 Torsion submodule 8 Torsion-free module 8 Torus 148 Total degree 468 Total order 2 Total pair 256 Total space, of fiber bundle 90 Total space, of fibration 66 Totally ordered set 2 Trace of endomorphism 9 Transgression 518—519 TREE 139 Triangulation 113 Triangulation, finer than covering 124 Triple, homology sequence of 184—185 201 Triple, homotopy sequence of 378 Trivial fiber bundle 92 Truncated polynomial algebra 264
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