K-Theory for operator algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge <<[u.a.]>>
Univ. Press
1998
|
| Edition: | 2. ed. |
| Series: | Publications / Mathematical Sciences Research Institute
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 300 S. |
| ISBN: | 0521635322 |
Staff View
MARC
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| 245 | 1 | 0 | |a K-Theory for operator algebras |c Bruce Blackadar |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge <<[u.a.]>> |b Univ. Press |c 1998 | |
| 300 | |a XX, 300 S. | ||
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Record in the Search Index
| _version_ | 1804140424694071296 |
|---|---|
| adam_text | JRT-THEORY FOR OPERATOR ALGEBRAS SECOND EDITION BRUCE BLACKADAR
UNIVERSITY OF NEVADA, RENO CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE
TO SECOND EDITION IX PREFACE TO FIRST EDITION XIII CHAPTER I.
INTRODUCTION TO TF-THEORY 1 1 SURVEY OF TOPOLOGICAL IF-THEORY 1 1.1
VECTOR BUNDLES 1 1.2 WHITNEY SUM 3 1.3 THE GROTHENDIECK GROUP 4 1.4 THE
TF-GROUPS 4 1.5 LOCALLY COMPACT SPACES 5 1.6 EXACT SEQUENCES 5 1.7
ALGEBRAIC FORMULATION OF /F-THEORY 7 2 OVERVIEW OF OPERATOR IF-THEORY 9
2.1 NONCOMMUTATIVE TOPOLOGY 9 2.2 THE IFO-FUNCTOR 10 2.3 THE /G-FUNCTOR
11 2.4 EXTENSIONS OF C*-ALGEBRAS 11 2.5 KK-THEORY 12 2.6 FURTHER
DEVELOPMENTS 13 CHAPTER II. PRELIMINARIES 15 3 LOCAL BANACH ALGEBRAS AND
INDUCTIVE LIMITS 15 3-1 LOCAL BANACH ALGEBRAS 15 3.2 UNITIZATION 16 3.3
INDUCTIVE LIMITS 17 3.4 INVERTIBLE ELEMENTS 18 4 IDEMPOTENTS AND
EQUIVALENCE 19 4.1 IDEMPOTENTS 20 4.2 EQUIVALENCE OF IDEMPOTENTS 20 4.3
ALGEBRAIC EQUIVALENCE, SIMILARITY, AND HOMOTOPY 20 4.4 SIMILARITY VS.
HOMOTOPY 21 4.5 EQUIVALENCE AND COMPLETION 22 XVI CONTENTS 4.6
PROJECTIONS 22 4.7 EXERCISES AND PROBLEMS 24 NOTES FOR CHAPTER II 25
CHAPTER III. TFO-THEORY AND ORDER 27 5 BASIC K 0 -THEOTY 27 5.1 BASIC
DEFINITIONS 27 5.2 PROPERTIES OF V(A) 28 5.3 PRELIMINARY DEFINITION OF
KQ 29 5.4 RELATIVE K-GROUPS 29 5.5 DEFINITION OF K 0 {A) 30 5.6
EXACTNESS OF K O 31 5.7 EXERCISES AND PROBLEMS 32 6 ORDER STRUCTURE ON K
O 32 6.1 INTRODUCTION 32 6.2 ORDERED GROUPS 33 6.3 K 0 (A) AS AN ORDERED
GROUP 34 6.4 CANCELLATION 36 6.5 STABLE RANK 36 6.6 CLASSIFICATION OF
STABLY ISOMORPHIC C*-ALGEBRAS 38 6.7 PERFORATION 39 6.8 STATES ON
ORDERED GROUPS 40 6.9 DIMENSION FUNCTIONS AND STATES ON KO(A) 41 6.10
EXERCISES AND PROBLEMS 42 6.11 PROPERLY INFINITE C*-ALGEBRAS 45 7 THEORY
OF AF ALGEBRAS 48 7.1 BASIC DEFINITIONS 48 7.2 REPRESENTATION BY
DIAGRAMS 49 7.3 DIMENSION GROUPS 49 7.4 CLASSIFICATION OF DIMENSION
GROUPS 51 7.5 UHF ALGEBRAS 52 7.6 OTHER SIMPLE AF ALGEBRAS 53 7.7
EXERCISES AND PROBLEMS 55 CHAPTER IV. TFI-THEORY AND BOTT PERIODICITY 59
8 HIGHER /^-GROUPS 59 8.1 DEFINITION OF KI(A) 59 8.2 SUSPENSIONS 61 8.3
LONG EXACT SEQUENCE OF K-THEORY 62 9 BOTT PERIODICITY 64 9.1 BASIC
DEFINITIONS 64 9.2 PROOF OF THE THEOREM 65 CONTENTS XVII 9.3 SIX-TERM
EXACT SEQUENCE 67 9.4 EXERCISES AND PROBLEMS 68 NOTES FOR CHAPTER IV 70
CHAPTER V. IF-THEORY OF CROSSED PRODUCTS 71 10 THE PIMSNER-VOICULESCU
EXACT SEQUENCE AND CONNES THORN ISOMOR- PHISM 71 10.1 CROSSED PRODUCTS
71 10.2 CROSSED PRODUCTS BY Z OR R 72 10.3 THE MAPPING TORUS 74 10.4
PROOF OF THE P-V SEQUENCE 75 10.5 HOMOTOPY INVARIANCE 76 10.6 EXACT
SEQUENCE FOR CROSSED PRODUCTS BY T 77 10.7 EXACT SEQUENCE FOR CROSSED
PRODUCTS BY FINITE CYCLIC GROUPS 77 10.8 CROSSED PRODUCTS BY AMALGAMATED
FREE PRODUCTS 78 10.9 PROOF OF THE THORN ISOMORPHISM 79 10.10 ORDER
STRUCTURE AND TRACES ON A X A Z 83 10.11 EXERCISES AND PROBLEMS 86 11
EQUIVARIANT IF-THEORY 92 11.1 GROUP ALGEBRAS 92 11.2 PROJECTIVE MODULES
93 11.3 PROJECTIONS 94 11.4 G- VECTOR BUNDLES 95 11.5 DEFINITION OF
EQUIVARIANT KO 95 11.6 HOMOTOPY INVARIANCE 96 11.7 RELATION WITH CROSSED
PRODUCTS 97 11.8 MODULE STRUCTURE ON K 0 (A X A G) 98 11.9 PROPERTIES OF
EQUIVARIANT IF-THEORY 99 11.10 EQUIVARIANT IF-THEORY FOR NONCOMPACT
GROUPS 100 11.11 EXERCISES AND PROBLEMS 100 CHAPTER VI. MORE
PRELIMINARIES 103 12 MULTIPLIER ALGEBRAS 103 12.1 INTRODUCTION 103 12.2
K-THEORY AND STABLE MULTIPLIER ALGEBRAS 104 12.3 CR-UNITAL C*-ALGEBRAS
105 12.4 KASPAROV S TECHNICAL THEOREM 105 12.5 EXERCISES AND PROBLEMS
107 13 HILBERT MODULES , 108 13.1 BASIC DEFINITIONS 108 13.2 BOUNDED
OPERATORS ON HILBERT MODULES 109 13.3 REGULAR OPERATORS 110 13.4 HILBERT
MODULES AND MULTIPLIER ALGEBRAS 110 XVIII CONTENTS 13.5 TENSOR PRODUCTS
OF HILBERT MODULES ILL 13.6 THE STABILIZATION OR ABSORPTION THEOREM ILL
13.7 EXERCISES AND PROBLEMS 113 14 GRADED C*-ALGEBRAS 114 14.1 BASIC
DEFINITIONS 114 14.2 GRADED HILBERT MODULES . 116 14.3 GRADED
HOMOMORPHISMS 116 14.4 GRADED TENSOR PRODUCTS 116 14.5 STRUCTURE OF
GRADED TENSOR PRODUCTS 118 14.6 MISCELLANEOUS THEOREMS 119 14.7
EXERCISES AND PROBLEMS 120 CHAPTER VII. THEORY OF EXTENSIONS 121 15
BASIC THEORY OF EXTENSIONS 121 15.1 BASIC DEFINITIONS 121 15.2 THE BUSBY
INVARIANT 122 15.3 PULLBACKS 122 15.4 EQUIVALENCE 123 15.5 TRIVIAL
EXTENSIONS 125 15.6 ADDITIVE STRUCTURE 126 15.7 INVERSES 128 15.8
NUCLEAR C*-ALGEBRAS 129 15.9 FUNCTORIALITY 131 15.10 HOMOTOPY INVARIANCE
131 15.11 BOTT PERIODICITY, EXACT SEQUENCES 132 15.12 ABSORBING
EXTENSIONS 132 15.13 EXTENSIONS OF GRADED C*- ALGEBRAS 134 15.14
EXTENSIONS AND IF-THEORY 134 16 BROWN-DOUGLAS-FILLMORE THEORY AND OTHER
APPLICATIONS 135 16.2 ESSENTIALLY NORMAL OPERATORS 135 16.3 EXT AS
TF-HOMOLOGY 137 16.4 EXERCISES AND PROBLEMS 139 CHAPTER VIII. KASPAROV S
TFTF-THEORY 143 17 BASIC THEORY 143 17.1 KASPAROV MODULES 143 17.2
EQUIVALENCE RELATIONS 147 17.3 THE KTF-GROUPS 149 17.4 STANDARD
SIMPLIFICATIONS , * 152 17.5 FREDHOLM PICTURE OF KK( A, B) 153 17.6
QUASIHOMOMORPHISM OR CUNTZ PICTURE OF KK(A, B) 155 17.7 ADDITIVITY 158
17.8 FUNCTORIALITY 158 CONTENTS XIX 17.9 HOMOTOPY INVARIANCE 161 17.10
COBORDISM AND ISOMORPHISM OF KK O H AND KK C 161 17.11 UNBOUNDED
KASPAROV MODULES 163 18 THE INTERSECTION PRODUCT 166 18.1 DESCRIPTION OF
THE PRODUCT 166 18.2 OUTLINE OF THE CONSTRUCTION 166 18.3 CONNECTIONS
169 18.4 CONSTRUCTION OF THE PRODUCT 172 18.5 ISOMORPHISM OF KK^ AND KK
O H 175 18.6 ASSOCIATIVITY 178 18.7 FUNCTORIALITY 179 18.8 RING
STRUCTURE ON KK(A, A) 179 18.9 GENERAL FORM OF THE PRODUCT 180 18.10
PRODUCTS ON KK 1 181 18.11 EXTENDIBILITY OF KK -ELEMENTS 183 18.12
RECAPITULATION 184 18.13 EXERCISES AND PROBLEMS 185 19 FURTHER STRUCTURE
IN KK-THEORY 187 19.1 KKT-EQUIVALENCE 187 19.2 BOTT PERIODICITY 189 19.3
THORN ISOMORPHISM 190 19.4 MAPPING CONES AND PUPPE SEQUENCES 193 19.5
EXACT SEQUENCES 195 19.6 PIMSNER-VOICULESCU EXACT SEQUENCES 198 19.7
COUNTABLE ADDITIVITY 199 19.8 RECAPITULATION 200 19.9 EXERCISES AND
PROBLEMS 201 20 EQUIVARIANT KK-THEORY 204 20.1 PRELIMINARIES 205 20.2
THE EQUIVARIANT KK-GROUPS 206 20.3 THE INTERSECTION PRODUCT 207 20.4 THE
REPRESENTATION RING 208 20.5 RESTRICTION AND INDUCTION 209 20.6 RELATION
WITH CROSSED PRODUCTS 210 20.7 CONNECTED GROUPS 211 20.8 DISCRETE GROUPS
213 20.9 K-THEORETIC AMENABILITY FOR GROUPS 213 20.10 EXERCISES AND
PROBLEMS 215 CHAPTER IX. FURTHER TOPICS 217 21 HOMOLOGY AND COHOMOLOGY
THEORIES ON C*- ALGEBRAS 217 21.1 BASIC DEFINITIONS 217 XX CONTENTS 21.2
MAYER-VIETORIS SEQUENCE 219 21.3 CONTINUITY 220 21.4 HALF-EXACT FUNCTORS
222 21.5 APPLICATIONS TO KK-THEOIY 223 22 AXIOMATIC TF-THEORY 224 22.1
KK AS A CATEGORY 225 22.2 UNIVERSAL ENVELOPING CATEGORIES 226 22.3
FUNCTORS ON KK AND AXIOMATIC K-THEORY 227 22.4 EXERCISES AND PROBLEMS
230 23 UNIVERSAL COEFFICIENT THEOREMS AND KIINNETH THEOREMS 232 23.1
STATEMENTS OF THE THEOREMS 232 23.2 PROOF OF THE SPECIAL UCT 234 23.3
PROOF OF THE SPECIAL KT 235 23.4 PROOF OF THE SPECIAL KTP 235 23.5
GEOMETRIC RESOLUTIONS OF C*-ALGEBRAS 236 23.6 PROOF OF THE GENERAL KTP
238 23.7 PROOF OF THE GENERAL KT 239 23.8 PROOF OF THE GENERAL UCT 239
23.9 NATURALITY 240 23.10 SOME COROLLARIES 240 23.11 SPLITTING 243 23.12
THE GENERAL KT 243 23.13 EXTENSIONS OF THE THEOREMS 243 23.14
EQUIVARIANT THEOREMS 244 23.15 EXERCISES AND PROBLEMS 245 24 SURVEY OF
APPLICATIONS TO GEOMETRY AND TOPOLOGY 248 24.1 INDEX THEOREMS 248 24.2
HOMOTOPY INVARIANCE OF HIGHER SIGNATURES 253 24.3 POSITIVE SCALAR
CURVATURE 255 24.4 THE BAUM-CONNES CONJECTURE 257 24.5 KK-THEORETIC
PROOFS 258 25 E-THEORY 260 25.1 ASYMPTOTIC MORPHISMS 261 25.2 TENSOR
PRODUCTS AND SUSPENSIONS 265 25.3 COMPOSITION 265 25.4 ADDITIVE
STRUCTURE 268 25.5 EXACT SEQUENCES 270 25.6 AXIOMATIC ^-THEORY 277 25.7
EXERCISES AND PROBLEMS 279 REFERENCES 283 INDEX 297
|
| any_adam_object | 1 |
| author | Blackadar, Bruce 1948- |
| author_GND | (DE-588)111248485 |
| author_facet | Blackadar, Bruce 1948- |
| author_role | aut |
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| classification_rvk | SK 600 |
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| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV024446147 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:59:46Z |
| institution | BVB |
| isbn | 0521635322 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018422864 |
| oclc_num | 632281282 |
| open_access_boolean | |
| owner | DE-83 DE-11 DE-188 |
| owner_facet | DE-83 DE-11 DE-188 |
| physical | XX, 300 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Univ. Press |
| record_format | marc |
| series2 | Publications / Mathematical Sciences Research Institute |
| spelling | Blackadar, Bruce 1948- Verfasser (DE-588)111248485 aut K-Theory for operator algebras Bruce Blackadar 2. ed. Cambridge <<[u.a.]>> Univ. Press 1998 XX, 300 S. txt rdacontent n rdamedia nc rdacarrier Publications / Mathematical Sciences Research Institute 5 K-Theorie (DE-588)4033335-8 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 s K-Theorie (DE-588)4033335-8 s DE-604 Mathematical Sciences Research Institute Publications 5 (DE-604)BV000013092 5 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018422864&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blackadar, Bruce 1948- K-Theory for operator algebras K-Theorie (DE-588)4033335-8 gnd Operatoralgebra (DE-588)4129366-6 gnd |
| subject_GND | (DE-588)4033335-8 (DE-588)4129366-6 |
| title | K-Theory for operator algebras |
| title_auth | K-Theory for operator algebras |
| title_exact_search | K-Theory for operator algebras |
| title_full | K-Theory for operator algebras Bruce Blackadar |
| title_fullStr | K-Theory for operator algebras Bruce Blackadar |
| title_full_unstemmed | K-Theory for operator algebras Bruce Blackadar |
| title_short | K-Theory for operator algebras |
| title_sort | k theory for operator algebras |
| topic | K-Theorie (DE-588)4033335-8 gnd Operatoralgebra (DE-588)4129366-6 gnd |
| topic_facet | K-Theorie Operatoralgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018422864&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000013092 |
| work_keys_str_mv | AT blackadarbruce ktheoryforoperatoralgebras |