An introduction to k-theory and cyclic cohomology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Warszawa
Polish Scientific Publishers
1998
|
| Series: | Advanced topics in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 128 Seiten |
| ISBN: | 8301124741 |
Staff View
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Record in the Search Index
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| adam_text | AND CYCLIC COHOMOLOGY JACEK BRODZKI POLISH SCIENTIFIC PUBLISHERS
WARSZAWA1998 CONTENTS 1. INTRODUCTION 9 2. THE AT-FUNCTOR IN VARIOUS
SITUATIONS 11 2.1. THE GROTHENDIECK GROUP 11 2.2. THE K-THEORY OF SPACES
13 2.2.1. THE SERRE-SWAN THEOREM 13 2.2.2. THE GROUP K(X) 15 2.2.3.
REDUCED K-THEORY 16 2.2.4. HOMOTOPY INVARIANCE AND EXCISION 17 2.2.5.
MORE ON THE SERRE-SWAN THEOREM 21 2.2.6. HIGHER I 2.3. ALGEBRAIC
IF-THEORY 26 2.3.1. KO(A) AND PROJECTIVE YL-MODULES 26 2.3.2. KI(A) AND
THE WHITEHEAD LEMMA 28 2.3.3. RELATIVE IF-GROUPS AND MILNOR S
CONSTRUCTION 29 2.3.4. RELATIVE .RT-GROUPS AND EXCISION 32 2.3.5.
QUILLEN S HIGHER ^-THEORY 34 2.4. /F-THEORY OF C*-ALGEBRAS 35 2.4.1.
ALGEBRAIC /^-THEORY OF C*-ALGEBRAS 38 2.5. IF-HOMOLOGY 39 3. CYCLIC
HOMOLOGY 44 3.1. NONCOMMUTATIVE DIFFERENTIAL FORMS 44 3.1.1.
DIFFERENTIAL FORMS AND THE KAROUBI OPERATOR 44 3.1.2. THE HARMONIC
DECOMPOSITION 49 3.1.3. CYCLIC HOMOLOGY 51 3.1.4. THE NONUNITAL CASE 55
3.2. DEFORMATIONS OF THE ALGEBRA OA 5 6 3.2.1. UNIVERSAL ALGEBRA
EXTENSIONS , 56 3.2.2. THE CUNTZ ALGEBRA QA 59 3.2.3. THE CUNTZ ALGEBRA
AND KK-THEORY 61 3.3. COCHAINS AND CHARACTERS 63 3.4. SUPERTRACES 65 4.
CHERN CHARACTERS 67 4.1. IF-THEORY AND CHERN CLASSES 67 4.2. ALGEBRAIC
CHERN-WEIL THEORY 68 4.3. HIGHER TRACES 72 4.4. EVEN HIGHER TRACES AND
KO(A) 73 4.5. TOEPLITZ OPERATORS . 75 4.6. ODD HIGHER TRACES AND KI(A)
77 5. EXCISION IN CYCLIC HOMOLOGY AND ALGEBRAIC .K-THEORY 82 5.1. THE
LODAY-QUILLEN THEOREM 82 5.2. EXCISION IN CYCLIC HOMOLOGY 88 5.3.
EXCISION IN ALGEBRAIC /F-THEORY 94 6. FURTHER EXAMPLES 97 6.1.
DERIVATIONS AND CYCLIC HOMOLOGY 97 6.2. CYCLIC AND REDUCED CYCLIC
HOMOLOGY 101 6.3. CANONICAL CLASSES IN REDUCED CYCLIC COHOMOLOGY 102
6.4. REDUCED CYCLIC COHOMOLOGY OF THE WEYL ALGEBRA 105 6.5. EXCISION IN
PERIODIC CYCLIC COHOMOLOGY 106 7. ENTIRE CYCLIC COHOMOLOGY OF BANACH
ALGEBRAS ILL 7.1. TOPOLOGY ON QA AND QA ILL 7.2. SIMPLICIAL
NORMALIZATION 114 7.2.1. A HOMOTOPY OF SUPERALGEBRAS 115 7.2.2. HOMOTOPY
OF SUPERTRACES 117 7.3. HOMOTOPY INVARIANCE OF ENTIRE CYCLIC COHOMOLOGY
119 7.4. DERIVATIONS AND ENTIRE CYCLIC COHOMOLOGY 121 7.5. THE JLO
COCYCLE : 122 BIBLIOGRAPHY 125 INDEX 128
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| indexdate | 2024-07-09T19:57:13Z |
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| isbn | 8301124741 |
| language | English |
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| physical | 128 Seiten |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Polish Scientific Publishers |
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| series2 | Advanced topics in mathematics |
| spelling | Brodzki, Jacek aut An introduction to k-theory and cyclic cohomology Jacek Brodzki Warszawa Polish Scientific Publishers 1998 128 Seiten txt rdacontent n rdamedia nc rdacarrier Advanced topics in mathematics Homology theory K-theory Algebraische K-Theorie (DE-588)4141839-6 gnd rswk-swf Zyklische Homologie (DE-588)4269326-3 gnd rswk-swf Algebraische K-Theorie (DE-588)4141839-6 s Zyklische Homologie (DE-588)4269326-3 s b DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012772831&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brodzki, Jacek An introduction to k-theory and cyclic cohomology Homology theory K-theory Algebraische K-Theorie (DE-588)4141839-6 gnd Zyklische Homologie (DE-588)4269326-3 gnd |
| subject_GND | (DE-588)4141839-6 (DE-588)4269326-3 |
| title | An introduction to k-theory and cyclic cohomology |
| title_auth | An introduction to k-theory and cyclic cohomology |
| title_exact_search | An introduction to k-theory and cyclic cohomology |
| title_full | An introduction to k-theory and cyclic cohomology Jacek Brodzki |
| title_fullStr | An introduction to k-theory and cyclic cohomology Jacek Brodzki |
| title_full_unstemmed | An introduction to k-theory and cyclic cohomology Jacek Brodzki |
| title_short | An introduction to k-theory and cyclic cohomology |
| title_sort | an introduction to k theory and cyclic cohomology |
| topic | Homology theory K-theory Algebraische K-Theorie (DE-588)4141839-6 gnd Zyklische Homologie (DE-588)4269326-3 gnd |
| topic_facet | Homology theory K-theory Algebraische K-Theorie Zyklische Homologie |
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