Characteristic classes and the cohomology of finite groups:
The purpose of this book is to study the relation between the representation ring of a finite group and its integral cohomology by means of characteristic classes. In this way it is possible to extend the known calculations and prove some general results for the integral cohomology ring of a group G...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1986
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
9 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | The purpose of this book is to study the relation between the representation ring of a finite group and its integral cohomology by means of characteristic classes. In this way it is possible to extend the known calculations and prove some general results for the integral cohomology ring of a group G of prime power order. Among the groups considered are those of p-rank less than 3, extra-special p-groups, symmetric groups and linear groups over finite fields. An important tool is the Riemann - Roch formula which provides a relation between the characteristic classes of an induced representation, the classes of the underlying representation and those of the permutation representation of the infinite symmetric group. Dr Thomas also discusses the implications of his work for some arithmetic groups which will interest algebraic number theorists. Dr Thomas assumes the reader has taken basic courses in algebraic topology, group theory and homological algebra, but has included an appendix in which he gives a purely topological proof of the Riemann - Roch formula |
| Beschreibung: | 1 Online-Ressource (xii, 129 Seiten) |
| ISBN: | 9780511897344 |
| DOI: | 10.1017/CBO9780511897344 |
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 9 | |
| 520 | |a The purpose of this book is to study the relation between the representation ring of a finite group and its integral cohomology by means of characteristic classes. In this way it is possible to extend the known calculations and prove some general results for the integral cohomology ring of a group G of prime power order. Among the groups considered are those of p-rank less than 3, extra-special p-groups, symmetric groups and linear groups over finite fields. An important tool is the Riemann - Roch formula which provides a relation between the characteristic classes of an induced representation, the classes of the underlying representation and those of the permutation representation of the infinite symmetric group. Dr Thomas also discusses the implications of his work for some arithmetic groups which will interest algebraic number theorists. Dr Thomas assumes the reader has taken basic courses in algebraic topology, group theory and homological algebra, but has included an appendix in which he gives a purely topological proof of the Riemann - Roch formula | ||
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Datensatz im Suchindex
| _version_ | 1804176880188784640 |
|---|---|
| any_adam_object | |
| author | Thomas, C. B. 1938-2005 |
| author_GND | (DE-588)138331472 |
| author_facet | Thomas, C. B. 1938-2005 |
| author_role | aut |
| author_sort | Thomas, C. B. 1938-2005 |
| author_variant | c b t cb cbt |
| building | Verbundindex |
| bvnumber | BV043940130 |
| classification_rvk | SK 260 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511897344 (OCoLC)967678385 (DE-599)BVBBV043940130 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511897344 |
| format | Electronic eBook |
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| id | DE-604.BV043940130 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:12Z |
| institution | BVB |
| isbn | 9780511897344 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349100 |
| oclc_num | 967678385 |
| open_access_boolean | |
| owner | DE-12 DE-92 DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR DE-83 |
| physical | 1 Online-Ressource (xii, 129 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Thomas, C. B. 1938-2005 Verfasser (DE-588)138331472 aut Characteristic classes and the cohomology of finite groups C.B. Thomas Characteristic Classes & the Cohomology of Finite Groups Cambridge Cambridge University Press 1986 1 Online-Ressource (xii, 129 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 9 The purpose of this book is to study the relation between the representation ring of a finite group and its integral cohomology by means of characteristic classes. In this way it is possible to extend the known calculations and prove some general results for the integral cohomology ring of a group G of prime power order. Among the groups considered are those of p-rank less than 3, extra-special p-groups, symmetric groups and linear groups over finite fields. An important tool is the Riemann - Roch formula which provides a relation between the characteristic classes of an induced representation, the classes of the underlying representation and those of the permutation representation of the infinite symmetric group. Dr Thomas also discusses the implications of his work for some arithmetic groups which will interest algebraic number theorists. Dr Thomas assumes the reader has taken basic courses in algebraic topology, group theory and homological algebra, but has included an appendix in which he gives a purely topological proof of the Riemann - Roch formula Finite groups Homology theory Characteristic classes Charakteristische Klasse (DE-588)4194231-0 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Homologietheorie (DE-588)4141714-8 gnd rswk-swf Kohomologie (DE-588)4031700-6 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Homologietheorie (DE-588)4141714-8 s Endliche Gruppe (DE-588)4014651-0 s DE-604 Kohomologie (DE-588)4031700-6 s Charakteristische Klasse (DE-588)4194231-0 s Gruppentheorie (DE-588)4072157-7 s Erscheint auch als Druck-Ausgabe 978-0-521-25661-2 Erscheint auch als Druck-Ausgabe 978-0-521-09065-0 Cambridge studies in advanced mathematics 9 (DE-604)BV044781283 9 https://doi.org/10.1017/CBO9780511897344 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Thomas, C. B. 1938-2005 Characteristic classes and the cohomology of finite groups Cambridge studies in advanced mathematics Finite groups Homology theory Characteristic classes Charakteristische Klasse (DE-588)4194231-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Homologietheorie (DE-588)4141714-8 gnd Kohomologie (DE-588)4031700-6 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| subject_GND | (DE-588)4194231-0 (DE-588)4072157-7 (DE-588)4141714-8 (DE-588)4031700-6 (DE-588)4014651-0 |
| title | Characteristic classes and the cohomology of finite groups |
| title_alt | Characteristic Classes & the Cohomology of Finite Groups |
| title_auth | Characteristic classes and the cohomology of finite groups |
| title_exact_search | Characteristic classes and the cohomology of finite groups |
| title_full | Characteristic classes and the cohomology of finite groups C.B. Thomas |
| title_fullStr | Characteristic classes and the cohomology of finite groups C.B. Thomas |
| title_full_unstemmed | Characteristic classes and the cohomology of finite groups C.B. Thomas |
| title_short | Characteristic classes and the cohomology of finite groups |
| title_sort | characteristic classes and the cohomology of finite groups |
| topic | Finite groups Homology theory Characteristic classes Charakteristische Klasse (DE-588)4194231-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Homologietheorie (DE-588)4141714-8 gnd Kohomologie (DE-588)4031700-6 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| topic_facet | Finite groups Homology theory Characteristic classes Charakteristische Klasse Gruppentheorie Homologietheorie Kohomologie Endliche Gruppe |
| url | https://doi.org/10.1017/CBO9780511897344 |
| volume_link | (DE-604)BV044781283 |
| work_keys_str_mv | AT thomascb characteristicclassesandthecohomologyoffinitegroups AT thomascb characteristicclassesthecohomologyoffinitegroups |