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Bibliographic Details
Main Author:	Bredon, Glen E. 1932-2000 (Author)
Format:	Book
Language:	German
Published:	New York [u.a.] Springer 1997
Edition:	2. ed.
Series:	Graduate texts in mathematics 170
Subjects:	Sheaf theory Homologie Kohomologie Garbentheorie Algebraische Topologie Garbe > Mathematik
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. 487 - 490
Physical Description:	XI, 502 S. graph. Darst.
ISBN:	0387949054 9781461268543

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adam_text	GLEN E. BREDON SHEAF THEORY SECOND EDITION SPRINGER CONTENTS PREFACE V I SHEAVES AND PRESHEAVES 1 1 DEFINITIONS 1 2 HOMOMORPHISMS, SUBSHEAVES, AND QUOTIENT SHEAVES . . . . 8 3 DIRECT AND INVERSE IMAGES 12 4 COHOMOMORPHISMS 14 5 ALGEBRAIC CONSTRUCTIONS 16 6 SUPPORTS 21 7 CLASSICAL COHOMOLOGY THEORIES 24 EXERCISES 30 II SHEAF COHOMOLOGY 33 1 DIFFERENTIAL SHEAVES AND RESOLUTIONS 34 2 THE CANONICAL RESOLUTION AND SHEAF COHOMOLOGY 36 3 INJECTIVE SHEAVES 41 4 ACYCLIC SHEAVES 46 5 FLABBY SHEAVES . 47 6 CONNECTED SEQUENCES OF FUNCTORS 52 7 AXIOMS FOR COHOMOLOGY AND THE CUP PRODUCT 56 8 MAPS OF SPACES * * * 61 9 $-SOFT AND $-FINE SHEAVES 65 10 SUBSPACES . . . . . . . . . . . . . . . . . . . . . 71 11 THE VIETORIS MAPPING THEOREM AND HOMOTOPY INVARIANCE . 75 12 RELATIVE COHOMOLOGY 83 13 MAYER-VIETORIS THEOREMS 94 14 CONTINUITY 100 15 THE KIINNETH AND UNIVERSAL COEFFICIENT THEOREMS 107 16 DIMENSION 110 17 LOCAL CONNECTIVITY . 126 18 CHANGE OF SUPPORTS; LOCAL COHOMOLOGY GROUPS 134 19 THE TRANSFER HOMOMORPHISM AND THE SMITH SEQUENCES ... 137 20 STEENROD S CYCLIC REDUCED POWERS 148 21 THE STEENROD OPERATIONS 162 EXERCISES 169 IX X CONTENTS III COMPARISON WITH OTHER COHOMOLOGY THEORIES 179 1 SINGULAR COHOMOLOGY 179 2 ALEXANDER-SPANIER COHOMOLOGY 185 3 DE RHAM COHOMOLOGY . . . . . . . .~ 187 4 CECH COHOMOLOGY 189 EXERCISES 194 IV APPLICATIONS OF SPECTRAL SEQUENCES 197 1 THE SPECTRAL SEQUENCE OF A DIFFERENTIAL SHEAF 198 2 THE FUNDAMENTAL THEOREMS OF SHEAVES 202 3 DIRECT IMAGE RELATIVE TO A SUPPORT FAMILY 210 4 THE LERAY SHEAF 213 5 EXTENSION OF A SUPPORT FAMILY BY A FAMILY ON THE BASE SPACE 219 6 THE LERAY SPECTRAL SEQUENCE OF A MAP 221 7 FIBER BUNDLES 227 8 DIMENSION 237 9 THE SPECTRAL SEQUENCES OF BOREL AND CARTAN 246 10 CHARACTERISTIC CLASSES 251 11 THE SPECTRAL SEQUENCE OF A FILTERED DIFFERENTIAL SHEAF 257 12 THE FARY SPECTRAL SEQUENCE 262 13 SPHERE BUNDLES WITH SINGULARITIES . . . . . . . . . . . . . . . 264 14 THE OLIVER TRANSFER AND THE CONNER CONJECTURE 267 EXERCISES 275 V BOREL-MOORE HOMOLOGY 279 1 COSHEAVES 281 2 THE DUAL OF A DIFFERENTIAL COSHEAF 289 3 HOMOLOGY THEORY 292 4 MAPS OF SPACES 299 5 SUBSPACES AND RELATIVE HOMOLOGY 303 6 THE VIETORIS THEOREM, HOMOTOPY, AND COVERING SPACES . . . 317 7 THE HOMOLOGY SHEAF OF A MAP 322 8 THE BASIC SPECTRAL SEQUENCES 324 9 POINCARE DUALITY 329 10 THE CAP PRODUCT 335 11 INTERSECTION THEORY 344 12 UNIQUENESS THEOREMS 349 13 UNIQUENESS THEOREMS FOR MAPS AND RELATIVE HOMOLOGY . . . . 358 14 THE KUNNETH FORMULA 364 15 CHANGE OF RINGS 368 16 GENERALIZED MANIFOLDS 373 17 LOCALLY HOMOGENEOUS SPACES 392 18 HOMOLOGICAL FIBRATIONS AND P-ADIC TRANSFORMATION GROUPS . . 394 19 THE TRANSFER HOMOMORPHISM IN HOMOLOGY 403 20 SMITH THEORY IN HOMOLOGY 407 EXERCISES 411 CONTENTS XI VI COSHEAVES AND CECH HOMOLOGY 417 1 THEORY OF COSHEAVES 418 2 LOCAL TRIVIALITY . . . . . . . . . . . . . . . . . . . . . . . . . 420 3 LOCAL ISOMORPHISMS 421 4 CECH HOMOLOGY 424 5 THE REFLECTOR 428 6 SPECTRAL SEQUENCES 431 7 CORESOLUTIONS 432 8 RELATIVE CECH HOMOLOGY 434 9 LOCALLY PARACOMPACT SPACES . . . . . . . . . . . . . . . . . . 438 10 BOREL-MOORE HOMOLOGY 439 11 MODIFIED BOREL-MOORE HOMOLOGY 442 12 SINGULAR HOMOLOGY 443 13 ACYCLIC COVERINGS 445 14 APPLICATIONS TO MAPS 446 EXERCISES 448 A SPECTRAL SEQUENCES 449 1 THE SPECTRAL SEQUENCE OF A FILTERED COMPLEX 449 2 DOUBLE COMPLEXES 451 3 PRODUCTS 453 4 HOMOMORPHISMS 454 B SOLUTIONS TO SELECTED EXERCISES 455 SOLUTIONS FOR CHAPTER I 455 SOLUTIONS FOR CHAPTER II 459 SOLUTIONS FOR CHAPTER III 472 SOLUTIONS FOR CHAPTER IV 473 SOLUTIONS FOR CHAPTER V 480 SOLUTIONS FOR CHAPTER VI . . 486 BIBLIOGRAPHY 487 LIST OF SYMBOLS 491 LIST OF SELECTED FACTS 493 INDEX 495
any_adam_object	1
author	Bredon, Glen E. 1932-2000
author_GND	(DE-588)1013248945
author_facet	Bredon, Glen E. 1932-2000
author_role	aut
author_sort	Bredon, Glen E. 1932-2000
author_variant	g e b ge geb
building	Verbundindex
bvnumber	BV011300351
callnumber-first	Q - Science
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ctrlnum	(OCoLC)246649907 (DE-599)BVBBV011300351
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dewey-ones	514 - Topology
dewey-raw	514.224
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dewey-sort	3514.224
dewey-tens	510 - Mathematics
discipline	Mathematik
edition	2. ed.
format	Book
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language	German
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series	Graduate texts in mathematics
series2	Graduate texts in mathematics
spelling	Bredon, Glen E. 1932-2000 Verfasser (DE-588)1013248945 aut Sheaf theory Glen E. Bredon 2. ed. New York [u.a.] Springer 1997 XI, 502 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 170 Literaturverz. S. 487 - 490 Sheaf theory Homologie (DE-588)4141951-0 gnd rswk-swf Kohomologie (DE-588)4031700-6 gnd rswk-swf Garbentheorie (DE-588)4155956-3 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Garbe Mathematik (DE-588)4019261-1 gnd rswk-swf Garbentheorie (DE-588)4155956-3 s DE-604 Garbe Mathematik (DE-588)4019261-1 s Algebraische Topologie (DE-588)4120861-4 s 1\p DE-604 Homologie (DE-588)4141951-0 s 2\p DE-604 Kohomologie (DE-588)4031700-6 s 3\p DE-604 Erscheint auch als Online-Ausgabe 978-1-4612-6854-3 Graduate texts in mathematics 170 (DE-604)BV000000067 170 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007590739&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Bredon, Glen E. 1932-2000 Sheaf theory Graduate texts in mathematics Sheaf theory Homologie (DE-588)4141951-0 gnd Kohomologie (DE-588)4031700-6 gnd Garbentheorie (DE-588)4155956-3 gnd Algebraische Topologie (DE-588)4120861-4 gnd Garbe Mathematik (DE-588)4019261-1 gnd
subject_GND	(DE-588)4141951-0 (DE-588)4031700-6 (DE-588)4155956-3 (DE-588)4120861-4 (DE-588)4019261-1
title	Sheaf theory
title_auth	Sheaf theory
title_exact_search	Sheaf theory
title_full	Sheaf theory Glen E. Bredon
title_fullStr	Sheaf theory Glen E. Bredon
title_full_unstemmed	Sheaf theory Glen E. Bredon
title_short	Sheaf theory
title_sort	sheaf theory
topic	Sheaf theory Homologie (DE-588)4141951-0 gnd Kohomologie (DE-588)4031700-6 gnd Garbentheorie (DE-588)4155956-3 gnd Algebraische Topologie (DE-588)4120861-4 gnd Garbe Mathematik (DE-588)4019261-1 gnd
topic_facet	Sheaf theory Homologie Kohomologie Garbentheorie Algebraische Topologie Garbe Mathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007590739&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000067
work_keys_str_mv	AT bredonglene sheaftheory

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