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Algebraic topology from a homotopical viewpoint / Marcelo Aguilar, Samuel Gitler, Carlos Prieto.

By: Aguilar, M. A. (Marcelo A.).
Contributor(s): Gitler, Samuel | Prieto, C. (Carlos).
Material type: TextTextSeries: Universitext.Publisher: New York : Springer, c2002Description: xxix, 478 p., E 79.95 ill. ; 25 cm.ISBN: 0387954503 (alk. paper).Subject(s): Algebraic topology | Homotopy theoryDDC classification: 514/.2 Online resources: Table of contents | Publisher description
Contents:
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.
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks 		514.2 AGU (Browse shelf) Available 8731
Total holds: 0

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.