Algebraic K-theory and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1996
|
| Edition: | Corr. 2. printing |
| Series: | Graduate texts in mathematics
147 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 392 S. |
| ISBN: | 3540942483 0387942483 |
Staff View
MARC
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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 |
| 250 | |a Corr. 2. printing | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a X, 392 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 147 | |
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Record in the Search Index
| _version_ | 1804125609502179328 |
|---|---|
| adam_text | Contents
Preface
Chapter
1.
Ko
oí Rings
1
1.
Defining
Ко
1
2.
Ko
from idempotents
7
3.
Ko
of
РШв
aud local
rings
11
4.
Ko
of Dedekind domains
16
5.
Relative
Ko
and excision
27
6.
An application: Swan s Theorem and
topologicei
К-
theory
32
7.
Another application:
Euler
characteristics and the Wall
ñniteness
obstruction
41
Chapter
2.
Ki of Rings
59
1.
Defining
ΑΊ
59
2.
K of division rings and local rings
62
3.
K of
РШѕ
and Dedekind domains
74
4.
Whitehead groups and Whitehead torsion
83
5.
Relative K and the exact sequence
92
Chapter
3.
Ко
and
ΑΊ
of Categories, Negative
Ä-Theory
108
1.
Kq and
Κι
of categories, Gq and G of rings
108
2.
The Grothendieck and Bass-Heller-Swan Theorems
132
3.
Negative Jf-theory
153
Chapter
4.
Milnor s K2
162
1.
Universal central extensions and
Щ
162
Universal central extensions
163
Homology of groups
168
2.
The Steinberg group
187
3.
Milnor s
Kt
199
4.
Applications of Ki
218
Computing certain relative
Κ χ
groups
218
Ki of fields and number theory
221
Almost commuting operators
237
Pseudo-isotopy
240
χ
Contents
Chapter
5.
The
+-
Construction and Quillen
iC-Theory
245
1.
An introduction to classifying spaces
245
2.
Quillen s +4;onstruction and its basic properties
265
3.
A survey of higher K-theary
279
Products
279
Jr-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
tf-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 Ko
335
The Chern character on higher K-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
|
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| id | DE-604.BV011116957 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:04:17Z |
| institution | BVB |
| isbn | 3540942483 0387942483 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007449561 |
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| physical | X, 392 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| 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 Corr. 2. printing New York [u.a.] Springer 1996 X, 392 S. 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 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007449561&sequence=000002&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=007449561&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT rosenbergjonathan algebraicktheoryanditsapplications |