A primer on mapping class groups:
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Princeton, N.J.
Princeton University Press
2012
|
Schriftenreihe: | Princeton mathematical series
49 |
Schlagworte: | |
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©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: | xiv, 472 p. |
Internformat
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100 | 1 | |a Farb, Benson |d 1967- |e Verfasser |0 (DE-588)1020817828 |4 aut | |
245 | 1 | 0 | |a A primer on mapping class groups |c Benson Farb and Dan Margalit |
264 | 1 | |a Princeton, N.J. |b Princeton University Press |c 2012 | |
300 | |a xiv, 472 p. | ||
336 | |b txt |2 rdacontent | ||
337 | |b c |2 rdamedia | ||
338 | |b cr |2 rdacarrier | ||
490 | 0 | |a Princeton mathematical series |v 49 | |
500 | |a Includes bibliographical references and index | ||
500 | |a "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©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 | ||
505 | 0 | |a pt. 1. Mapping class groups -- pt. 2. Teichmüller space and moduli space -- pt. 3. The classification and pseudo-Anosov theory | |
650 | 4 | |a Mappings (Mathematics) | |
650 | 4 | |a Class groups (Mathematics) | |
650 | 0 | 7 | |a Klassengruppe |0 (DE-588)4164018-4 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Klassifikation |0 (DE-588)4030958-7 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Teichmüller-Raum |0 (DE-588)4131425-6 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Teichmüller-Modulgruppe |0 (DE-588)4319741-3 |2 gnd |9 rswk-swf |
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650 | 0 | 7 | |a Homöomorphismus |0 (DE-588)4352383-3 |2 gnd |9 rswk-swf |
689 | 0 | 0 | |a Teichmüller-Modulgruppe |0 (DE-588)4319741-3 |D s |
689 | 0 | 1 | |a Teichmüller-Raum |0 (DE-588)4131425-6 |D s |
689 | 0 | |8 1\p |5 DE-604 | |
689 | 1 | 0 | |a Homöomorphismus |0 (DE-588)4352383-3 |D s |
689 | 1 | 1 | |a Klassifikation |0 (DE-588)4030958-7 |D s |
689 | 1 | |8 2\p |5 DE-604 | |
689 | 2 | 0 | |a Abbildung |g Mathematik |0 (DE-588)4000044-8 |D s |
689 | 2 | 1 | |a Klassengruppe |0 (DE-588)4164018-4 |D s |
689 | 2 | |8 3\p |5 DE-604 | |
700 | 1 | |a Margalit, Dan |d 1976- |e Sonstige |0 (DE-588)1020818212 |4 oth | |
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Datensatz im Suchindex
_version_ | 1804177942781100032 |
---|---|
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 | BV044566418 |
collection | ZDB-30-PAD |
contents | pt. 1. Mapping class groups -- pt. 2. Teichmüller space and moduli space -- pt. 3. The classification and pseudo-Anosov theory |
ctrlnum | (ZDB-30-PAD)EBC744105 (ZDB-89-EBL)EBL744105 (ZDB-38-EBR)ebr10492894 (OCoLC)745866891 (DE-599)BVBBV044566418 |
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 |
format | Electronic eBook |
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id | DE-604.BV044566418 |
illustrated | Not Illustrated |
indexdate | 2024-07-10T07:56:06Z |
institution | BVB |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029964942 |
oclc_num | 745866891 |
open_access_boolean | |
physical | xiv, 472 p. |
psigel | ZDB-30-PAD |
publishDate | 2012 |
publishDateSearch | 2012 |
publishDateSort | 2012 |
publisher | Princeton University Press |
record_format | marc |
series2 | Princeton mathematical series |
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 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©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 pt. 1. Mapping class groups -- pt. 2. Teichmüller space and moduli space -- pt. 3. The classification and pseudo-Anosov theory Mappings (Mathematics) Class groups (Mathematics) Klassengruppe (DE-588)4164018-4 gnd rswk-swf Klassifikation (DE-588)4030958-7 gnd rswk-swf Teichmüller-Raum (DE-588)4131425-6 gnd rswk-swf Teichmüller-Modulgruppe (DE-588)4319741-3 gnd rswk-swf Abbildung Mathematik (DE-588)4000044-8 gnd rswk-swf Homöomorphismus (DE-588)4352383-3 gnd rswk-swf Teichmüller-Modulgruppe (DE-588)4319741-3 s Teichmüller-Raum (DE-588)4131425-6 s 1\p DE-604 Homöomorphismus (DE-588)4352383-3 s Klassifikation (DE-588)4030958-7 s 2\p DE-604 Abbildung Mathematik (DE-588)4000044-8 s Klassengruppe (DE-588)4164018-4 s 3\p DE-604 Margalit, Dan 1976- Sonstige (DE-588)1020818212 oth 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Farb, Benson 1967- A primer on mapping class groups pt. 1. Mapping class groups -- pt. 2. Teichmüller space and moduli space -- pt. 3. The classification and pseudo-Anosov theory Mappings (Mathematics) Class groups (Mathematics) Klassengruppe (DE-588)4164018-4 gnd Klassifikation (DE-588)4030958-7 gnd Teichmüller-Raum (DE-588)4131425-6 gnd Teichmüller-Modulgruppe (DE-588)4319741-3 gnd Abbildung Mathematik (DE-588)4000044-8 gnd Homöomorphismus (DE-588)4352383-3 gnd |
subject_GND | (DE-588)4164018-4 (DE-588)4030958-7 (DE-588)4131425-6 (DE-588)4319741-3 (DE-588)4000044-8 (DE-588)4352383-3 |
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 | Mappings (Mathematics) Class groups (Mathematics) Klassengruppe (DE-588)4164018-4 gnd Klassifikation (DE-588)4030958-7 gnd Teichmüller-Raum (DE-588)4131425-6 gnd Teichmüller-Modulgruppe (DE-588)4319741-3 gnd Abbildung Mathematik (DE-588)4000044-8 gnd Homöomorphismus (DE-588)4352383-3 gnd |
topic_facet | Mappings (Mathematics) Class groups (Mathematics) Klassengruppe Klassifikation Teichmüller-Raum Teichmüller-Modulgruppe Abbildung Mathematik Homöomorphismus |
work_keys_str_mv | AT farbbenson aprimeronmappingclassgroups AT margalitdan aprimeronmappingclassgroups |