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Algebraic topology:

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Bibliographic Details
Main Author:	Spanier, Edwin Henry 1921-1996 (Author)
Format:	Book
Language:	English
Published:	New York u.a. Springer 1989
Edition:	2. print.
Subjects:	Algebraic topology Algebraische Topologie Lehrbuch
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 528 S.
ISBN:	3540906460 0387906460 0387944265

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MARC


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Record in the Search Index

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adam_text	EDWIN H. SPANIER ALGEBRAIC TOPOLOGY SPRINGER CONTENTS INTRODUCTION I 1 SET THEORY 1 2 GENERAL TOPOLOGY 4 ! 3 GROUP THEORY 6 4 MODULES 7 5 EUCLIDEAN SPACES 9 1 HOMOTOPY AND THE FUNDAMENTAL GROUP 12 1 CATEGORIES 14 2 FUNCTORS 18 3 HOMOTOPY 22 4 RETRACTION AND DEFORMATION 27 5 H SPACES 33 6 SUSPENSION 39 7 THE FUNDAMENTAL GROUPOID 45 8 THE FUNDAMENTAL GROUP SO EXERCISES 56 *** CONTENTS 2 COVERING SPACES AND FIBRATIONS 6O 1 COVERING PROJECTIONS 62 2 THE HOMOTOPY LIFTING PROPERTY 65 3 RELATIONS WITH THE FUNDAMENTAL GROUP 70 4 THE LIFTING PROBLEM 74 5 THE CLASSIFICATION OF COVERING PROJECTIONS 79 6 COVERING TRANSFORMATIONS 85. 7 FIBER BUNDLES 89 8 FIBRATIONS 96 EXERCISES 103 POLYHEDRA 1O6 1 SIMPLIDAL COMPLEXES 108 2 LINEARITY IN SIMPLIDAL COMPLEXES 114 3 SUBDIVISION 121 4 SIMPLIDAL APPROXIMATION 126 5 CONTIGUITY CLASSES 129 6 THE EDGE-PATH GROUPOID 134 I 7 GRAPHS 139 8 EXAMPLES AND APPLICATIONS 143 EXERCISES 149 HOMOLOGY 15 4 1 CHAIN COMPLEXES 156 2 CHAIN HOMOTOPY 162 & 3 THE HOMOLOGY OF SIMPLIDAL COMPLEXES 167 4 SINGULAR HOMOLOGY 173 5 EXACTNESS 179 MAYER-VIETORIS SEQUENCES 186 7 SOME APPLICATIONS OF HOMOLOGY 193 8 AXIOMATIC CHARACTERIZATION OF HOMOLOGY 199 EXERCISES 205 CONTENTS XITI 5 PRODUCTS 21 1 HOMOLOGY WITH COEFFICIENTS 212 2 THE UNIVERSAL-COEFFIDEHT THEOREM FOR HOMOLOGY 219 3 THE KUNNETH FORMULA 227 4 COHOMOLOGY 236 5 THE UNIVERSAL-COEFFIDENT THEOREM FOR COHOMOLOGY 241 CUP AND CAP PRODUCTS 248 7 HOMOLOGY OF FIBER BUNDLES 255 8 THE COHOMOLOGY ALGEBRA 263 9 THE STEENROD SQUARING OPERATIONS 269 EXERCISES 276 6 GENERAL COHOMOLOG Y THEORY AN D DUALITY 284 1 THE SLANT PRODUCT 286 2 DUALITY IN TOPOLOGICAL MANIFOLDS 292 YY 3 THE FUNDAMENTAL CLASS OF A MANIFOLD 299 4 THE ALEXANDER COHOMOLOGY THEORY 306 5 THE HOMOTOPY AXIOM FOR THE ALEXANDER THEORY 311 6 TAUTNESS AND CONTINUITY 315 7 PRESHEAVES 323 8 FINE PRESHEAVES 329 9 APPLICATIONS OF THE COHOMOLOGY OF PRESHEAVES 338 1 CHARACTERISTIC CLASSES 346 EXERCISES 356 HOMOTOPY THEORY 38 2 1 EXACT SEQUENCES OF SETS OF HOMOTOPY CLASSES 364 2 HIGHER HOMOTOPY GROUPS 371 YY 3 CHANGE OF BASE POINTS 379 4 THE HUREWICZ HOMOMORPHISM 387 5 THE HUREWICZ ISOMORPHISM THEOREM 393 6 CW COMPLEXES 400 7 HOMOTOPY FUNCTORS 406 8 WEAK HOMOTOPY TYPE 412 EXERCISES 418 XIV CONTENTS 8 OBSTRUCTION THEORY 42 2 1 EILENBERG-MACLANE SPACES 424 2 PRINCIPAL FIBRATIONS 432 3 MOORE-POSTNIKOV FACTORIZATIONS 437 4 OBSTRUCTION THEORY 445 5 THE SUSPENSION MAP 452 EXERCISES 460 9 SPECTRAL SEQUENCES AND HOMOTOPY GROUPS OF SPHERES 46 4 1 SPECTRAL SEQUENCES 466 2 THE SPECTRAL SEQUENCE OF A FIBRATION 473 3 APPLICATIONS OF THE HOMOLOGY SPECTRAL SEQUENCE 481 4 MULTIPLICATIVE PROPERTIES OF SPECTRAL SEQUENCES- 490 5 APPLICATIONS OF THE COHOMOLOGY SPECTRAL SEQUENCE 498 S SERRE CLASSES OF ABELIAN GROUPS 504 7 HOMOTOPY GROUPS OF SPHERES 512 EXERCISES 518 INDEX 52 1
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author	Spanier, Edwin Henry 1921-1996
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indexdate	2024-07-09T17:45:25Z
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isbn	3540906460 0387906460 0387944265
language	English
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spelling	Spanier, Edwin Henry 1921-1996 Verfasser (DE-588)11565819X aut Algebraic topology Edwin H. Spanier 2. print. New York u.a. Springer 1989 XIV, 528 S. txt rdacontent n rdamedia nc rdacarrier Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Algebraische Topologie (DE-588)4120861-4 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006658938&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Spanier, Edwin Henry 1921-1996 Algebraic topology Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd
subject_GND	(DE-588)4120861-4 (DE-588)4123623-3
title	Algebraic topology
title_auth	Algebraic topology
title_exact_search	Algebraic topology
title_full	Algebraic topology Edwin H. Spanier
title_fullStr	Algebraic topology Edwin H. Spanier
title_full_unstemmed	Algebraic topology Edwin H. Spanier
title_short	Algebraic topology
title_sort	algebraic topology
topic	Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd
topic_facet	Algebraic topology Algebraische Topologie Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006658938&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT spanieredwinhenry algebraictopology

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