A primer on mapping class groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J
Princeton University Press
2012
|
| Schriftenreihe: | Princeton mathematical series
49 |
| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 UBM01 UPA01 Volltext |
| Beschreibung: | Includes bibliographical references and index "The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.The book begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichm(c)oller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification"--Provided by publisher |
| Beschreibung: | 1 Online-Ressource (xiv, 472 p) |
| ISBN: | 9781400839049 |
| DOI: | 10.1515/9781400839049 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804174888913600512 |
|---|---|
| any_adam_object | |
| author | Farb, Benson 1967- |
| author_GND | (DE-588)1020817828 (DE-588)1020818212 |
| author_facet | Farb, Benson 1967- |
| author_role | aut |
| author_sort | Farb, Benson 1967- |
| author_variant | b f bf |
| building | Verbundindex |
| bvnumber | BV042693253 |
| classification_rvk | SK 260 |
| collection | ZDB-23-DGG |
| ctrlnum | (OCoLC)745866891 (DE-599)GBV68129728X |
| dewey-full | 512.7/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/4 |
| dewey-search | 512.7/4 |
| dewey-sort | 3512.7 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400839049 |
| format | Electronic eBook |
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| id | DE-604.BV042693253 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:07:33Z |
| institution | BVB |
| isbn | 9781400839049 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028124872 |
| oclc_num | 745866891 |
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| owner_facet | DE-859 DE-860 DE-Aug4 DE-19 DE-BY-UBM DE-739 DE-1046 DE-1043 DE-858 |
| physical | 1 Online-Ressource (xiv, 472 p) |
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| spelling | Farb, Benson 1967- Verfasser (DE-588)1020817828 aut A primer on mapping class groups Benson Farb and Dan Margalit Princeton, N.J Princeton University Press 2012 1 Online-Ressource (xiv, 472 p) txt rdacontent c rdamedia cr rdacarrier Princeton mathematical series 49 Includes bibliographical references and index "The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.The book begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichm(c)oller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification"--Provided by publisher Class groups (Mathematics) Mappings (Mathematics) Teichmüller-Modulgruppe (DE-588)4319741-3 gnd rswk-swf Klassengruppe (DE-588)4164018-4 gnd rswk-swf Homöomorphismus (DE-588)4352383-3 gnd rswk-swf Teichmüller-Raum (DE-588)4131425-6 gnd rswk-swf Abbildung Mathematik (DE-588)4000044-8 gnd rswk-swf Klassifikation (DE-588)4030958-7 gnd rswk-swf Teichmüller-Modulgruppe (DE-588)4319741-3 s Teichmüller-Raum (DE-588)4131425-6 s DE-604 Homöomorphismus (DE-588)4352383-3 s Klassifikation (DE-588)4030958-7 s Abbildung Mathematik (DE-588)4000044-8 s Klassengruppe (DE-588)4164018-4 s 1\p DE-604 Margalit, Dan 1976- Sonstige (DE-588)1020818212 oth https://doi.org/10.1515/9781400839049 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Farb, Benson 1967- A primer on mapping class groups Class groups (Mathematics) Mappings (Mathematics) Teichmüller-Modulgruppe (DE-588)4319741-3 gnd Klassengruppe (DE-588)4164018-4 gnd Homöomorphismus (DE-588)4352383-3 gnd Teichmüller-Raum (DE-588)4131425-6 gnd Abbildung Mathematik (DE-588)4000044-8 gnd Klassifikation (DE-588)4030958-7 gnd |
| subject_GND | (DE-588)4319741-3 (DE-588)4164018-4 (DE-588)4352383-3 (DE-588)4131425-6 (DE-588)4000044-8 (DE-588)4030958-7 |
| title | A primer on mapping class groups |
| title_auth | A primer on mapping class groups |
| title_exact_search | A primer on mapping class groups |
| title_full | A primer on mapping class groups Benson Farb and Dan Margalit |
| title_fullStr | A primer on mapping class groups Benson Farb and Dan Margalit |
| title_full_unstemmed | A primer on mapping class groups Benson Farb and Dan Margalit |
| title_short | A primer on mapping class groups |
| title_sort | a primer on mapping class groups |
| topic | Class groups (Mathematics) Mappings (Mathematics) Teichmüller-Modulgruppe (DE-588)4319741-3 gnd Klassengruppe (DE-588)4164018-4 gnd Homöomorphismus (DE-588)4352383-3 gnd Teichmüller-Raum (DE-588)4131425-6 gnd Abbildung Mathematik (DE-588)4000044-8 gnd Klassifikation (DE-588)4030958-7 gnd |
| topic_facet | Class groups (Mathematics) Mappings (Mathematics) Teichmüller-Modulgruppe Klassengruppe Homöomorphismus Teichmüller-Raum Abbildung Mathematik Klassifikation |
| url | https://doi.org/10.1515/9781400839049 |
| work_keys_str_mv | AT farbbenson aprimeronmappingclassgroups AT margalitdan aprimeronmappingclassgroups |