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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 1995
Edition:	3., corr. print.
Subjects:	Algebraische Topologie Lehrbuch
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 528 S.
ISBN:	0387944265 0387906460 3540906460

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MARC


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Record in the Search Index

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adam_text	CONTENTS INTRODUCTION I 1 Set theory 1 2 General topology 4 3 Group theory 6 4 Modules 7 5 Euclidean spaces 9 1 HOMOTOPV AND THE FUNDAMENTAL GROUP IS 1 Categories 14 2 Functors 18 3 Homotopy 22 4 Retraction and deformation 27 5 Hspaces 33 β Suspension 39 7 The fundamental groupoid 45 8 The fundamental group 50 Exercises 56 xi xii contents 2 COVERIN« SPACES AN» VIBRATIONS ·Ο 1 Covering projections 62 2 The homotopy Ufting 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 Fibrattons 96 Exercises 103 POLVHEDBA 1·β 1 Simplicial complexes 108 2 Linearity in simplicial complexes 114 3 Subdivision 121 4 Simplicial approximation 126 5 Contiguity classes 129 β The edge-pefh groupoid 134 7 Graphs 139 8 Examples and applications 143 Exercises 149 HOMOLOG Y 184 1 Chain complexes 156 2 Chain homotopy 162 3 The homohgy of simplicial complexes 167 4 Singular homohgy 173 5 Exactness 179 β Mayer-Vietoris sequences 186 7 Some applications of homohgy 193 8 Axiomatic characterization of homohgy 199 Exercises 205 CONTENTS ХІІІ 5 PRODUCTS 21β 1 Homology with coefficients 212 2 The universal-coefficient theorem, for homohgy 219 3 The Künneth formula 227 4 Cohomohgy 236 6 The universal-coefficient theorem, for cohomohgy 241 β Cup and cap products 248 7 Homology of fiber bundles 255 8 The cohomohgy algebra 263 О The Steenrod squaring operations 269 Exercises 276 6 GENERAL COBOMOLOSY THEORY AN» DUALITY 3*4 1 The slant product 286 2 Duality in topohgical manifolds 292 3 The fundamental class of a manifold 299 4 The Alexander cohomology theory 306 5 The homotopy axiom for the Alexander theory 311 β Tautness and continuity 315 7 Presheaves 323 8 Fine presheaves 329 9 Applications of the cóhomology of presheaves 338 10 Characteristic classes 346 Exercises 356 HOMOTOPY THEORY 3«3 1 Exact sequences of sets of homotopy classes 364 2 Higher homotopy groups 371 3 Change of base points 379 4 The Hurewicz homomorphism 387 5 The Hurewicz isomorphism theorem 393 β CWcomplexes 400 7 Homotopy functors 406 Я Weak homotopy type 412 Exercise» 418 MV CONTENTS 8 OBSTRUCTION THEORY 423 1 EÜenberg-MacLane spaces 424 2 Principal fibrations 432 3 Moore-Postnikov factorizations 437 4 Obstruction theory 445 5 The suspension map 452 Exercises 4вО €F SPECTRAL SEQUENCES AND HOMOTOPV GROUPS OF SPHERES 4«4 1 Spectral sequences 466 2 The spectral sequence of a fibration 473 3 Applications of the homoiogy spectral sequence 481 4 Multiplicative properties of spectral sequences 490 5 Applications of the cohomology spectral sequence 498 β Sen« classes of abelian groups 504 7 Homotopy groups of spheres 512 Exercises 518 INDEX SSI
adam_txt	CONTENTS INTRODUCTION I 1 Set theory 1 2 General topology 4 3 Group theory 6 4 Modules 7 5 Euclidean spaces 9 1 HOMOTOPV AND THE FUNDAMENTAL GROUP IS 1 Categories 14 2 Functors 18 3 Homotopy 22 4 Retraction and deformation 27 5 Hspaces 33 β Suspension 39 7 The fundamental groupoid 45 8 The fundamental group 50 Exercises 56 xi xii contents 2 COVERIN« SPACES AN» VIBRATIONS ·Ο 1 Covering projections 62 2 The homotopy Ufting 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 Fibrattons 96 Exercises 103 POLVHEDBA 1·β 1 Simplicial complexes 108 2 Linearity in simplicial complexes 114 3 Subdivision 121 4 Simplicial approximation 126 5 Contiguity classes 129 β The edge-pefh groupoid 134 7 Graphs 139 8 Examples and applications 143 Exercises 149 HOMOLOG Y 184 1 Chain complexes 156 2 Chain homotopy 162 3 The homohgy of simplicial complexes 167 4 Singular homohgy 173 5 Exactness 179 β Mayer-Vietoris sequences 186 7 Some applications of homohgy 193 8 Axiomatic characterization of homohgy 199 Exercises 205 CONTENTS ХІІІ 5 PRODUCTS 21β 1 Homology with coefficients 212 2 The universal-coefficient theorem, for homohgy 219 3 The Künneth formula 227 4 Cohomohgy 236 6 The universal-coefficient theorem, for cohomohgy 241 β Cup and cap products 248 7 Homology of fiber bundles 255 8 The cohomohgy algebra 263 О The Steenrod squaring operations 269 Exercises 276 6 GENERAL COBOMOLOSY THEORY AN» DUALITY 3*4 1 The slant product 286 2 Duality in topohgical manifolds 292 3 The fundamental class of a manifold 299 4 The Alexander cohomology theory 306 5 The homotopy axiom for the Alexander theory 311 β Tautness and continuity 315 7 Presheaves 323 8 Fine presheaves 329 9 Applications of the cóhomology of presheaves 338 10 Characteristic classes 346 Exercises 356 HOMOTOPY THEORY 3«3 1 Exact sequences of sets of homotopy classes 364 2 Higher homotopy groups 371 3 Change of base points 379 4 The Hurewicz homomorphism 387 5 The Hurewicz isomorphism theorem 393 β CWcomplexes 400 7 Homotopy functors 406 Я Weak homotopy type 412 Exercise» 418 MV CONTENTS 8 OBSTRUCTION THEORY 423 1 EÜenberg-MacLane spaces 424 2 Principal fibrations 432 3 Moore-Postnikov factorizations 437 4 Obstruction theory 445 5 The suspension map 452 Exercises 4вО €F SPECTRAL SEQUENCES AND HOMOTOPV GROUPS OF SPHERES 4«4 1 Spectral sequences 466 2 The spectral sequence of a fibration 473 3 Applications of the homoiogy spectral sequence 481 4 Multiplicative properties of spectral sequences 490 5 Applications of the cohomology spectral sequence 498 β Sen« classes of abelian groups 504 7 Homotopy groups of spheres 512 Exercises 518 INDEX SSI
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author	Spanier, Edwin Henry 1921-1996
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discipline	Mathematik
discipline_str_mv	Mathematik
edition	3., corr. print.
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isbn	0387944265 0387906460 3540906460
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spelling	Spanier, Edwin Henry 1921-1996 Verfasser (DE-588)11565819X aut Algebraic topology Edwin H. Spanier 3., corr. print. New York [u.a.] Springer 1995 XIV, 528 S. txt rdacontent n rdamedia nc rdacarrier 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 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014154521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Spanier, Edwin Henry 1921-1996 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_exact_search_txtP	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	Algebraische Topologie (DE-588)4120861-4 gnd
topic_facet	Algebraische Topologie Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014154521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT spanieredwinhenry algebraictopology

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