2666

Aguilar, M. A.(Marcelo A.)

Marcelo Aguilar, Samuel Gitler, Carlos Prieto

Springer

c2002

xxix, 478 p. ill.

Universitext

Includes bibliographical references (p. 457-462) and index. , Machine generated contents note: 1 FUNCTION SPACES 1 -- 11 Admissible Topologies 1 -- 12 Compact-Open Topology 2 -- 13 The Exponential Law 3 -- 2 CONNECTEDNESS AND -- ALGEBRAIC INVARIANTS 9 -- 21 Path Connectedness 9 -- 22 Homotopy Classes 10 -- 23 Topological Groups 13 -- 24 Homotopy of Mappings of the Circle into Itself 15 -- 25 The Fundamental Group 28 -- 26 The fundamental Group of the Circle 41 -- 27 H-Spaces 45 -- 28 Loop Spaces 48 -- 29 H-Cospaces 50 -- 210 Suspensions 53 -- 3 HOMOTOPY GROUPS 59 -- 31 Attaching Spaces; Cylinders and Cones 59 -- 32 The Seifert-van Kampen Theorem 63 -- 33 Homotopy Sequences I 72 -- 34 Homotopy Groups 80 -- 35 Homotopy Sequences II 84 -- 4 HOMOTOPY EXTENSION AND -- LIFTING PROPERTIES 89 -- 41 Cofibrations 89 -- 42 Some Results on Cofibrations 95 -- 43 Fibrations 101 -- 44 Pointed and Unpointed Homotopy Classes 119 -- 45 Locally Trivial Bundles 125 -- 46 Classification of Covering Maps over Paracompact Spaces 138 -- 5 CW-COMPLEXES AND HOMOLOGY 149 -- 51 CW-Complexes 149 -- 52 Infinite Symmetric Products 167 -- 53 Homology Groups 176 -- 6 HOMOTOPY PROPERTIES OF -- CW-COMPLEXES 189 -- 61 Eilenberg-Mac Lane and Moore Spaces 189 -- 62 Homotopy Excision and Related Results 193 -- 63 Homotopy Properties of the Moore spaces 201 -- 64 Homotopy Properties of the Eilenberg-Mac Lane spaces 217 -- 7 COHOMOLOGY GROUPS AND -- RELATED TOPICS 227 -- 71 Cohomology Groups 227 -- 72 Multiplication in Cohomology 238 -- 73 Cellular Homology and Cohomology 243 -- 74 Exact Sequences in Homology and Cohomology 252 -- 8 VECTOR BUNDLES 259 -- 81 Vector Bundles 259 -- 82 Projections and Vector Bundles 268 -- 83 Grassmann Manifolds and Universal Bundles 271 -- 84 Classification of Vector Bundles of Finite Type 276 -- 85 Classification of Vector Bundles over Paracompact Spaces 279 -- 9 K-THEORY 289 -- 91 Grothendieck Construction 289 -- 92 Definition of K(B) 292 -- 93 K(B) and Stable Equivalence of Vector Bundles 295 -- 94 Representations of K(B) and K(B) 299 -- 95 Bott Periodicity and Applications 302 -- 10 ADAMS OPERATIONS AND APPLICATIONS 309 -- 101 Definition of the Adams Operations 309 -- 102 The Splitting Principle 313 -- 103 Normed Algebras 315 -- 104 Division Algebras 317 -- 105 Multiplicative Structures on Rn and on S- 319 -- 106 The Hopf Invariant 321 -- 11 RELATIONS BETWEEN COHOMOLOGY AND -- VECTOR BUNDLES 331 -- 111 Contractibility of S00 332 -- 112 Description of K(Z/2, 1) 334 -- 113 Classification of Real Line Bundles 337 -- 114 Description of K(Z, 2) 340 -- 115 Classification of Complex Line Bundles 343 -- 116 Characteristic Classes 345 -- 117 Thom Isomorphism and Gysin Sequence 349 -- 118 Construction of Characteristic Classes and Applications 366 -- 12 COHOMOLOGY THEORIES AND -- BROWN REPRESENTABILITY 383 -- 121 Generalized Cohomology Theories 383 -- 122 Brown Representability Theorem 394 -- 123 Spectra 406 -- A PROOF OF THE DOLD-THOM THEOREM 421 -- A1 Criteria for Quasifibrations 421 -- A2 Symmetric Products 431 -- A3 Proof of the Dold-Thom Theorem 434 -- B PROOF OF THE -- BOTT PERIODICITY THEOREM 437 -- B1 A Convenient Description of BU x Z 437 -- B2 Proof of the Bott Periodicity Theorem 440

Gitler, Samuel. , Prieto, C.

514

.2

Ag932a

0387954503