Algebraic K-theory and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
1994
|
| Series: | Graduate Texts in Mathematics
147 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 392 Seiten |
| ISBN: | 3540942483 0387942483 |
Staff View
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| 100 | 1 | |a Rosenberg, Jonathan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Algebraic K-theory and its applications |c Jonathan Rosenberg |
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Record in the Search Index
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|---|---|
| adam_text |
JONATHAN ROSENBERG
ALGEBRAIC
K-THEORY
AND
ITS APPLICATIONS
SPRINGER-VERLAG
NEW
YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO
HONG KONG BARCELONA BUDAPEST
CONTENTS
PREFACE V
CHAPTER 1.
KO
OF RINGS 1
1.
DEFINING
KO
1
2.
K
0
FROM IDEMPOTENTS 7
3.
K
0
OF PIDS AND LOCAL RINGS 11
4.
KO
OF DEDEKIND DOMAINS 16
5.
RELATIVE
KO
AND EXCISION 27
6. AN APPLICATION: SWAN'S THEOREM AND TOPOLOGICAL
UET-THEORY
32
7.
ANOTHER APPLICATION: EULER CHAXACTERISTICS AND THE WALL
FINITENESS
OBSTRUCTION 41
CHAPTER
2.
K\
OF
RINGS
1.
DEFINING
K\
2.
K\
OF
DIVISION RINGS
AND
LOCAL RINGS
3.
KI
OF
PIDS
AND
DEDEKIND DOMAINS
4.
WHITEHEAD GROUPS
AND
WHITEHEAD TORSION
5.
RELATIVE
K\
AND THE
EXACT SEQUENCE
CHAPTER
3.
K
0
AND
K\
OF
CATEGORIES, NEGATIVE
K-THEORY
1.
KO
AND
K\
OF
CATEGORIES,
GQ
AND
G\
OF
RINGS
2.
THE
GROTHENDIECK
AND
BASS-HELLER-SWAN THEOREMS
3.
NEGATIVE IF-THEORY
CHAPTER
4.
MILNOR'S
KI
1.
UNIVERSAL CENTRAL EXTENSIONS
AND
H^
UNIVERSAL
CENTRAL EXTENSIONS
HOMOLOGY
OF
GROUPS
2.
THE
STEINBERG GROUP
3.
MILNOR'S
K
2
4.
APPLICATIONS
OF
K2
COMPUTING CERTAIN RELATIVE
K\
GROUPS
K2
OF
FIELDS
AND
NUMBER THEORY
ALMOST
COMMUTING OPERATORS
PSEUDO-ISOTOPY
59
59
62
74
83
92
108
108
132
153
162
162
163
168
187
199
218
218
221
237
240
X CONTENTS
CHAPTER 5.
THE +-CONSTRUCTION AND QUILLEN
TF-THEORY
245
1.
AN INTRODUCTION TO CLASSIFYING SPACES 245
2.
QUILLEN'S +-CONSTRUCTION AND ITS BASIC PROPERTIES 265
3.
A SURVEY OF HIGHER AE"-THEORY 279
PRODUCTS 279
UEF-THEORY OF FIELDS AND OF RINGS OF INTEGERS 281
THE Q-CONSTRUCTION AND RESULTS PROVED WITH IT 289
APPLICATIONS 295
CHAPTER 6.
CYCLIC HOMOLOGY AND ITS RELATION TO
AT-THEORY
302
1.
BASICS OF CYCLIC HOMOLOGY 302
HOCHSCHILD HOMOLOGY 302
CYCLIC HOMOLOGY 306
CONNECTIONS WITH "NON-COMMUTATIVE DE RHAM THEORY" 325
2.
THE CHERN CHARACTER 331
THE CLASSICAL CHERN CHARACTER 332
THE CHERN CHARACTER ON
KQ
335
THE CHERN CHARACTER ON HIGHER AE"-THEORY 340
3.
SOME APPLICATIONS 350
NON-VANISHING OF CLASS GROUPS AND WHITEHEAD GROUPS 350
IDEMPOTENTS
IN C*-ALGEBRAS 355
GROUP RINGS AND ASSEMBLY MAPS 362
REFERENCES 369
BOOKS AND MONOGRAPHS ON RELATED AREAS OF ALGEBRA,
ANALYSIS,
NUMBER THEORY, AND TOPOLOGY 369
BOOKS AND MONOGRAPHS ON ALGEBRAIC IF-THEORY 371
SPECIALIZED
REFERENCES 372
NOTATIONAL INDEX 377
SUBJECT INDEX
383 |
| any_adam_object | 1 |
| author | Rosenberg, Jonathan |
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| callnumber-first | Q - Science |
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| ctrlnum | (OCoLC)246648906 (DE-599)BVBBV009654902 |
| 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 |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2025-01-07T13:02:54Z |
| institution | BVB |
| isbn | 3540942483 0387942483 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006383994 |
| oclc_num | 246648906 |
| open_access_boolean | |
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| physical | X, 392 Seiten |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Graduate Texts in Mathematics |
| series2 | Graduate Texts in Mathematics |
| spelling | Rosenberg, Jonathan Verfasser aut Algebraic K-theory and its applications Jonathan Rosenberg New York, NY [u.a.] Springer 1994 X, 392 Seiten txt rdacontent n rdamedia nc rdacarrier Graduate Texts in Mathematics 147 K-theory Algebraische K-Theorie (DE-588)4141839-6 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 s DE-604 Graduate Texts in Mathematics 147 (DE-604)BV000000067 147 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006383994&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosenberg, Jonathan Algebraic K-theory and its applications Graduate Texts in Mathematics K-theory Algebraische K-Theorie (DE-588)4141839-6 gnd |
| subject_GND | (DE-588)4141839-6 |
| title | Algebraic K-theory and its applications |
| title_auth | Algebraic K-theory and its applications |
| title_exact_search | Algebraic K-theory and its applications |
| title_full | Algebraic K-theory and its applications Jonathan Rosenberg |
| title_fullStr | Algebraic K-theory and its applications Jonathan Rosenberg |
| title_full_unstemmed | Algebraic K-theory and its applications Jonathan Rosenberg |
| title_short | Algebraic K-theory and its applications |
| title_sort | algebraic k theory and its applications |
| topic | K-theory Algebraische K-Theorie (DE-588)4141839-6 gnd |
| topic_facet | K-theory Algebraische K-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006383994&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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