Topics in algebraic and topological K-theory:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Tagungsbericht Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Lecture notes in mathematics
2008 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVI, 302 S. graph. Darst. |
| ISBN: | 9783642157073 |
Internformat
MARC
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| 245 | 1 | 0 | |a Topics in algebraic and topological K-theory |c Paul Frank Baum ... Ed.: Guillermo Cortiñas |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
| 300 | |a XVI, 302 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 2008 | |
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Datensatz im Suchindex
| _version_ | 1805095071765233664 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
.AF-THEORY FOR GROUP C*-ALGEBRAS PAUL F. BAUM, RUBEN J. SANCHEZ-GARCIA 1
1 INTRODUCTION 1
2 C*-ALGEBRAS 2
2.1 DEFINITIONS 2
2.2 EXAMPLES 3
2.3 THE REDUCED C*-ALGEBRA OF A GROUP 4
2.4 TWO CLASSICAL THEOREMS 6
2.5 THE CATEGORICAL VIEWPOINT 6
3 /"-THEORY OF C*-ALGEBRAS 7
3.1 DEFINITION FOR UNITAL C*-ALGEBRAS 7
3.2 BOTT PERIODICITY 8
3.3 DEFINITION FOR NON-UNITAL C-ALGEBRAS 8
3.4 FUNCTORIALITY 9
3.5 MORE ON BOTT PERIODICITY 9
3.6 TOPOLOGICAL /T-THEORY 10
4 PROPER G-SPACES 11
5 CLASSIFYING SPACE FOR PROPER ACTIONS 12
5.1 EXAMPLES 13
6 EQUIVARIANT AT-HOMOLOGY 14
6.1 DEFINITIONS 14
6.2 FUNCTORIALITY 18
6.3 THE INDEX MAP 18
7 THE DISCRETE CASE 19
7.1 EQUIVARIANT /T-HOMOLOGY 19
7.2 SOME RESULTS ON DISCRETE GROUPS 20
7.3 COROLLARIES OF THE BAUM-CONNES CONJECTURE 21
8 THE COMPACT CASE 21
9 EQUIVARIANT /T-HOMOLOGY FOR G-C*-ALGEBRAS 22
10 THE CONJECTURE WITH COEFFICIENTS 24
XIII
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1005454728
DIGITALISIERT DURCH
IMAGE 2
XIV CONTENTS
11 HUBERT MODULES 25
11.1 DEFINITIONS AND EXAMPLES 26
11.2 THE REDUCED CROSSED-PRODUCT C* R (G,A) 28
11.3 PUSH-FORWARD OF HUBERT MODULES 30
12 HOMOTOPY MADE PRECISE AND /"/"-THEORY 30
13 EQUIVARIANT KK -THEORY 33
14 THE INDEX MAP 35
14.1 THE KASPAROV PRODUCT 35
14.2 THE KASPAROV DESCENT MAP 35
14.3 DEFINITION OF THE INDEX MAP 36
14.4 THE INDEX MAP WITH COEFFICIENTS 36
15 A BRIEF HISTORY OF /"-THEORY 37
15.1 THE /"-THEORY GENEALOGY TREE 37
15.2 THE HIRZEBRUCH-RIEMANN-ROCH THEOREM 38
15.3 THE UNITY OF A"-THEORY 39
REFERENCES 40
UNIVERSAL COEFFICIENT THEOREMS AND ASSEMBLY MAPS IN KK-THEORY RALF MEYER
45
1 INTRODUCTION 45
2 KASPAROV THEORY AND BAUM-CONNES CONJECTURE 46
2.1 KASPAROV THEORY VIA ITS UNIVERSAL PROPERTY 46
2.2 SUBCATEGORIES IN AA G 60
3 HOMOLOGICAL ALGEBRA 65
3.1 HOMOLOGICAL IDEALS IN TRIANGULATED CATEGORIES 67
3.2 FROM HOMOLOGICAL IDEALS TO DERIVED FUNCTORS 72
3.3 UNIVERSAL COEFFICIENT THEOREMS 93
REFERENCES 100
ALGEBRAIC V. TOPOLOGICAL /F-THEORY: A FRIENDLY MATCH GUILLERMO CORTINAS
103
1 INTRODUCTION 103
2 THE GROUPS K N FOR N 1 104
2.1 DEFINITION AND BASIC PROPERTIES OF K FOR J = 0,1 104
2.2 MATRIX-STABLE FUNCTORS 110
2.3 SUM RINGS AND INFINITE SUM RINGS 112
2.4 THE EXCISION SEQUENCE FOR KQ AND K\ 113
2.5 NEGATIVE /"-THEORY 116
3 TOPOLOGICAL /^-THEORY 117
3.1 TOPOLOGICAL K -THEORY OF BANACH ALGEBRAS 118
3.2 BOTT PERIODICITY 121
4 POLYNOMIAL HOMOTOPY AND KAROUBI-VILLAMAYOR K -THEORY 123 5 HOMOTOPY
AT-THEORY 126
5.1 DEFINITION AND BASIC PROPERTIES OF KH 126
5.2 KH FOR KO-REGULAR RINGS 128
5.3 TOEPLITZ RING AND THE FUNDAMENTAL THEOREM FOR KH 129
IMAGE 3
CONTENTS XV
6 QUILLEN'S HIGHER /"-THEORY 131
6.1 CLASSIFYING SPACES 131
6.2 PERFECT GROUPS AND THE PLUS CONSTRUCTION FOR BG 132
6.3 FUNCTORIALITY ISSUES 136
6.4 RELATIVE /"-GROUPS AND EXCISION 136
6.5 LOCALLY CONVEX ALGEBRAS 138
6.6 FRECHET M-ALGEBRAS WITH APPROXIMATE UNITS 139
6.7 FUNDAMENTAL THEOREM AND THE TOEPLITZ RING 140
7 COMPARISON BETWEEN ALGEBRAIC AND TOPOLOGICAL /"-THEORY I 142 7.1
STABLE C*-ALGEBRAS 142
7.2 STABLE BANACH ALGEBRAS 143
8 TOPOLOGICAL /"-THEORY FOR LOCALLY CONVEX ALGEBRAS 144
8.1 DIFFEOTOPY KV 144
8.2 DIFFEOTOPY K-THEORY 146
8.3 BOTT PERIODICITY 147
9 COMPARISON BETWEEN ALGEBRAIC AND TOPOLOGICAL K- THEORY II 149 9.1 THE
DIFFEOTOPY INVARIANCE THEOREM 149
9.2 KH OF STABLE LOCALLY CONVEX ALGEBRAS 151
10 AT-THEORY SPECTRA 152
10.1 QUILLEN'S /"-THEORY SPECTRUM 152
10.2 AV-THEORY SPACES 153
10.3 THE HOMOTOPY A"-THEORY SPECTRUM 155
11 PRIMARY AND SECONDARY CHERN CHARACTERS 156
11.1 CYCLIC HOMOLOGY 156
11.2 PRIMARY CHERN CHARACTER AND INFINITESIMAL K -THEORY 157 11.3
SECONDARY CHERN CHARACTERS 158
11.4 APPLICATION TO KD 160
12 COMPARISON BETWEEN ALGEBRAIC AND TOPOLOGICAL /^-THEORY III 160 12.1
STABLE FRECHET ALGEBRAS 160
12.2 STABLE LOCALLY CONVEX ALGEBRAS: THE COMPARISON SEQUENCE 161
REFERENCES 163
HIGHER ALGEBRAIC /^-THEORY ( A F T ER Q U I L L E N, THOMASON AND O T H
E R S)
MARCO SCHLICHTING 167
1 INTRODUCTION 167
2 THE /"-THEORY OF EXACT CATEGORIES 168
2.1 THE GROTHENDIECK GROUP OF AN EXACT CATEGORY 168
2.2 QUILLEN'S G-CONSTRUCTION AND HIGHER K-THEORY 172
2.3 QUILLEN'S FUNDAMENTAL THEOREMS 177
2.4 NEGATIVE /F-GROUPS 180
3 ALGEBRAIC /^-THEORY AND TRIANGULATED CATEGORIES 183
3.1 THE GROTHENDIECK-GROUP OF A TRIANGULATED CATEGORY 183 3.2 THE
THOMASON-WALDHAUSEN LOCALIZATION THEOREM 187 3.3 QUILLEN'S FUNDAMENTAL
THEOREMS REVISITED 197
IMAGE 4
XVI CONTENTS
3.4 THOMASON'S MAYER-VIETORIS PRINCIPLE 201
3.5 PROJECTIVE BUNDLE THEOREM AND REGULAR BLOW-UPS 207 4 BEYOND
TRIANGULATED CATEGORIES 211
4.1 STATEMENT OF RESULTS 211
A APPENDIX 215
A.I BACKGROUND FROM TOPOLOGY 215
A.2 BACKGROUND ON TRIANGULATED CATEGORIES 219
A.3 THE DERIVED CATEGORY OF QUASI-COHERENT SHEAVES 226
A.4 PROOF OF COMPACT GENERATION OF D Z QCOH(X) 230
REFERENCES 237
LECTURES ON DG-CATEGORIES TOEN BERTRAND 243
1 INTRODUCTION 243
2 LECTURE 1 : DG-CATEGORIES AND LOCALIZATION 244
2.1 THE GABRIEL-ZISMAN LOCALIZATION 244
2.2 BAD BEHAVIOR OF THE GABRIEL-ZISMAN LOCALIZATION 247
2.3 DG-CATEGORIES AND DG-FUNCTORS 250
2.4 LOCALIZATIONS AS A DG-CATEGORY 265
3 LECTURE 2: MODEL CATEGORIES AND DG-CATEGORIES 265
3.1 REMINDERS ON MODEL CATEGORIES 266
3.2 MODEL CATEGORIES AND DG-CATEGORIES 271
4 LECTURE 3: STRUCTURE OF THE HOMOTOPY CATEGORY OF DG-CATEGORIES 275 4.1
MAPS IN THE HOMOTOPY CATEGORY OF DG-CATEGORIES 276
4.2 EXISTENCE OF INTERNAL HORNS 280
4.3 EXISTENCE OF LOCALIZATIONS 281
4.4 TRIANGULATED DG-CATEGORIES 284
5 LECTURE 4: SOME APPLICATIONS 288
5.1 FUNCTORIAL CONES 288
5.2 SOME INVARIANTS 291
5.3 DESCENT 293
5.4 SATURATED DG-CATEGORIES AND SECONDARY K-THEORY 295
REFERENCES 301 |
| any_adam_object | 1 |
| author2 | Cortiñas, Guillermo |
| author2_role | edt |
| author2_variant | g c gc |
| author_GND | (DE-588)142972002 (DE-588)142972169 |
| author_facet | Cortiñas, Guillermo |
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| dewey-full | 512.66 514.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 514 - Topology |
| dewey-raw | 512.66 514.23 |
| dewey-search | 512.66 514.23 |
| dewey-sort | 3512.66 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Conference Proceeding Book |
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| spelling | Topics in algebraic and topological K-theory Paul Frank Baum ... Ed.: Guillermo Cortiñas Berlin [u.a.] Springer 2011 XVI, 302 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2008 Topologische K-Theorie (DE-588)4334283-8 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2007 Sedano gnd-content Algebraische K-Theorie (DE-588)4141839-6 s Topologische K-Theorie (DE-588)4334283-8 s DE-604 Baum, Paul Frank Sonstige (DE-588)142972002 oth Cortiñas, Guillermo (DE-588)142972169 edt Winter School on K-Theory 2007 Valle de Sedano Sonstige (DE-588)16094761-3 oth Erscheint auch als Online-Ausgabe 978-3-642-15708-0 Lecture notes in mathematics 2008 (DE-604)BV000676446 2008 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3521320&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020766440&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Topics in algebraic and topological K-theory Lecture notes in mathematics Topologische K-Theorie (DE-588)4334283-8 gnd Algebraische K-Theorie (DE-588)4141839-6 gnd |
| subject_GND | (DE-588)4334283-8 (DE-588)4141839-6 (DE-588)1071861417 |
| title | Topics in algebraic and topological K-theory |
| title_auth | Topics in algebraic and topological K-theory |
| title_exact_search | Topics in algebraic and topological K-theory |
| title_full | Topics in algebraic and topological K-theory Paul Frank Baum ... Ed.: Guillermo Cortiñas |
| title_fullStr | Topics in algebraic and topological K-theory Paul Frank Baum ... Ed.: Guillermo Cortiñas |
| title_full_unstemmed | Topics in algebraic and topological K-theory Paul Frank Baum ... Ed.: Guillermo Cortiñas |
| title_short | Topics in algebraic and topological K-theory |
| title_sort | topics in algebraic and topological k theory |
| topic | Topologische K-Theorie (DE-588)4334283-8 gnd Algebraische K-Theorie (DE-588)4141839-6 gnd |
| topic_facet | Topologische K-Theorie Algebraische K-Theorie Konferenzschrift 2007 Sedano |
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