Generalized cohomology:
"In the 1950s, Eilenberg and Steenrod presented their famous characterization of homology theory by seven axioms. Somewhat later, it was found that keeping just the first six of these axioms (all except the condition on the 'homology' of the point), one can obtain many other interesti...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Japanese |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
c2006
|
| Schriftenreihe: | Translations of mathematical monographs
230 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "In the 1950s, Eilenberg and Steenrod presented their famous characterization of homology theory by seven axioms. Somewhat later, it was found that keeping just the first six of these axioms (all except the condition on the 'homology' of the point), one can obtain many other interesting systems of algebraic invariants of topological manifolds, such as K-theory, cobordisms, and others. These theories come under the common name of generalized homology (or cohomology) theories. The purpose of the book is to give an exposition of generalized (co)homology theories that can be read by a wide group of mathematicians who are not experts in algebraic topology. It starts with basic notions of homotopy theory and then introduces the axioms of generalized (co)homology theory. Then the authors discuss various types of generalized cohomology theories, such as complex-oriented cohomology theories and Chern classes, K-theory, complex cobordisms, and formal group laws. A separate chapter is devoted to spectral sequences and their use in generalized cohomology theories. The book is intended to serve as an introduction to the subject for mathematicians who do not have advanced knowledge of algebraic topology. Prerequisites include standard graduate courses in algebra and topology, with some knowledge of ordinary homology theory and homotopy theory." -- Book cover. |
| Beschreibung: | Includes bibliographical references (p. 241-249) and index |
| Beschreibung: | xi, 254 p. 22 cm |
| ISBN: | 0821835149 |
Internformat
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| 240 | 1 | 0 | |a Ippan kohomorojī |
| 245 | 1 | 0 | |a Generalized cohomology |c Akira Kono ; Dai Tamaki ; translated by Dai Tamaki |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c c2006 | |
| 300 | |a xi, 254 p. |c 22 cm | ||
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| 520 | 3 | |a "In the 1950s, Eilenberg and Steenrod presented their famous characterization of homology theory by seven axioms. Somewhat later, it was found that keeping just the first six of these axioms (all except the condition on the 'homology' of the point), one can obtain many other interesting systems of algebraic invariants of topological manifolds, such as K-theory, cobordisms, and others. These theories come under the common name of generalized homology (or cohomology) theories. The purpose of the book is to give an exposition of generalized (co)homology theories that can be read by a wide group of mathematicians who are not experts in algebraic topology. It starts with basic notions of homotopy theory and then introduces the axioms of generalized (co)homology theory. Then the authors discuss various types of generalized cohomology theories, such as complex-oriented cohomology theories and Chern classes, K-theory, complex cobordisms, and formal group laws. A separate chapter is devoted to spectral sequences and their use in generalized cohomology theories. The book is intended to serve as an introduction to the subject for mathematicians who do not have advanced knowledge of algebraic topology. Prerequisites include standard graduate courses in algebra and topology, with some knowledge of ordinary homology theory and homotopy theory." -- Book cover. | |
| 650 | 4 | |a Homologie | |
| 650 | 4 | |a Opérations cohomologiques | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Cohomology operations | |
| 650 | 0 | 7 | |a Homologietheorie |0 (DE-588)4141714-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kohomologieoperation |0 (DE-588)4164608-3 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Kohomologieoperation |0 (DE-588)4164608-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Tamaki, Dai |e Sonstige |4 oth | |
| 830 | 0 | |a Translations of mathematical monographs |v 230 |w (DE-604)BV000002394 |9 230 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-014997281 | ||
Datensatz im Suchindex
| _version_ | 1804135659089166336 |
|---|---|
| adam_text | Contents
Preface to the English Edition
Preface
Chapter
1. NDR
2.
3.
4.
5. Freudenthal
6. Hopf
7.
Chapter
1.
2.
3.
4.
5.
6.
Chapter
1.
2.
3.
4.
5.
6.
7.
8.
9.
vi
Chapter
1.
2.
3.
4.
5.
6.
7.
8.
and Algebraic A -theory
9.
10.
Chapter
1.
2.
3.
of Spectral Sequences
4.
5.
6.
Chapter
1.
2.
3.
Appendix A. Simplicial Techniques
1.
2.
Appendix B. Limits
1.
2.
Appendix C. Spectrum
1.
2.
Bibliography
Index
|
| adam_txt |
Contents
Preface to the English Edition
Preface
Chapter
1. NDR
2.
3.
4.
5. Freudenthal
6. Hopf
7.
Chapter
1.
2.
3.
4.
5.
6.
Chapter
1.
2.
3.
4.
5.
6.
7.
8.
9.
vi
Chapter
1.
2.
3.
4.
5.
6.
7.
8.
and Algebraic A'-theory
9.
10.
Chapter
1.
2.
3.
of Spectral Sequences
4.
5.
6.
Chapter
1.
2.
3.
Appendix A. Simplicial Techniques
1.
2.
Appendix B. Limits
1.
2.
Appendix C. Spectrum
1.
2.
Bibliography
Index |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Kono, Akira |
| author_facet | Kono, Akira |
| author_role | aut |
| author_sort | Kono, Akira |
| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV021784548 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.3 |
| callnumber-search | QA612.3 |
| callnumber-sort | QA 3612.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 320 |
| ctrlnum | (OCoLC)62282755 (DE-599)BVBBV021784548 |
| dewey-full | 514/.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.23 |
| dewey-search | 514/.23 |
| dewey-sort | 3514 223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV021784548 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:42:37Z |
| indexdate | 2024-07-09T20:44:01Z |
| institution | BVB |
| isbn | 0821835149 |
| language | English Japanese |
| lccn | 2005057056 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014997281 |
| oclc_num | 62282755 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-11 |
| physical | xi, 254 p. 22 cm |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs Iwanami series in modern mathematics |
| spelling | Kono, Akira Verfasser aut Ippan kohomorojī Generalized cohomology Akira Kono ; Dai Tamaki ; translated by Dai Tamaki Providence, R.I. American Mathematical Society c2006 xi, 254 p. 22 cm txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 230 Iwanami series in modern mathematics Includes bibliographical references (p. 241-249) and index "In the 1950s, Eilenberg and Steenrod presented their famous characterization of homology theory by seven axioms. Somewhat later, it was found that keeping just the first six of these axioms (all except the condition on the 'homology' of the point), one can obtain many other interesting systems of algebraic invariants of topological manifolds, such as K-theory, cobordisms, and others. These theories come under the common name of generalized homology (or cohomology) theories. The purpose of the book is to give an exposition of generalized (co)homology theories that can be read by a wide group of mathematicians who are not experts in algebraic topology. It starts with basic notions of homotopy theory and then introduces the axioms of generalized (co)homology theory. Then the authors discuss various types of generalized cohomology theories, such as complex-oriented cohomology theories and Chern classes, K-theory, complex cobordisms, and formal group laws. A separate chapter is devoted to spectral sequences and their use in generalized cohomology theories. The book is intended to serve as an introduction to the subject for mathematicians who do not have advanced knowledge of algebraic topology. Prerequisites include standard graduate courses in algebra and topology, with some knowledge of ordinary homology theory and homotopy theory." -- Book cover. Homologie Opérations cohomologiques Homology theory Cohomology operations Homologietheorie (DE-588)4141714-8 gnd rswk-swf Kohomologieoperation (DE-588)4164608-3 gnd rswk-swf Homologietheorie (DE-588)4141714-8 s Kohomologieoperation (DE-588)4164608-3 s DE-604 Tamaki, Dai Sonstige oth Translations of mathematical monographs 230 (DE-604)BV000002394 230 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014997281&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kono, Akira Generalized cohomology Translations of mathematical monographs Homologie Opérations cohomologiques Homology theory Cohomology operations Homologietheorie (DE-588)4141714-8 gnd Kohomologieoperation (DE-588)4164608-3 gnd |
| subject_GND | (DE-588)4141714-8 (DE-588)4164608-3 |
| title | Generalized cohomology |
| title_alt | Ippan kohomorojī |
| title_auth | Generalized cohomology |
| title_exact_search | Generalized cohomology |
| title_exact_search_txtP | Generalized cohomology |
| title_full | Generalized cohomology Akira Kono ; Dai Tamaki ; translated by Dai Tamaki |
| title_fullStr | Generalized cohomology Akira Kono ; Dai Tamaki ; translated by Dai Tamaki |
| title_full_unstemmed | Generalized cohomology Akira Kono ; Dai Tamaki ; translated by Dai Tamaki |
| title_short | Generalized cohomology |
| title_sort | generalized cohomology |
| topic | Homologie Opérations cohomologiques Homology theory Cohomology operations Homologietheorie (DE-588)4141714-8 gnd Kohomologieoperation (DE-588)4164608-3 gnd |
| topic_facet | Homologie Opérations cohomologiques Homology theory Cohomology operations Homologietheorie Kohomologieoperation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014997281&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT konoakira ippankohomoroji AT tamakidai ippankohomoroji AT konoakira generalizedcohomology AT tamakidai generalizedcohomology |