Braids, links, and mapping class groups:
The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
1975
|
| Schriftenreihe: | Annals of Mathematics Studies
number 82 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400881420 |
| DOI: | 10.1515/9781400881420 |
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| 490 | 1 | |a Annals of Mathematics Studies |v number 82 | |
| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) | ||
| 520 | |a The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Birman, Joan S. 1927- |
| author_GND | (DE-588)1089320590 |
| author_facet | Birman, Joan S. 1927- |
| author_role | aut |
| author_sort | Birman, Joan S. 1927- |
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| dewey-full | 514/.224 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.224 |
| dewey-search | 514/.224 |
| dewey-sort | 3514 3224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400881420 |
| format | Electronic eBook |
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| id | DE-604.BV043712402 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:08Z |
| institution | BVB |
| isbn | 9781400881420 |
| language | English |
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| spelling | Birman, Joan S. 1927- (DE-588)1089320590 aut Braids, links, and mapping class groups Joan S. Birman Princeton, NJ Princeton University Press 1975 © 1974 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 82 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix In English Braid theory Knot theory Representations of groups Kette Mathematik (DE-588)4163681-8 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Zopf Mathematik (DE-588)4191043-6 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Darstellungstheorie (DE-588)4148816-7 s 1\p DE-604 Kette Mathematik (DE-588)4163681-8 s 2\p DE-604 Zopf Mathematik (DE-588)4191043-6 s 3\p DE-604 Knoten Mathematik (DE-588)4164314-8 s 4\p DE-604 Gruppe Mathematik (DE-588)4022379-6 s 5\p DE-604 Erscheint auch als Druck-Ausgabe 0-691-08149-2 Annals of Mathematics Studies number 82 (DE-604)BV040389493 82 https://doi.org/10.1515/9781400881420?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 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 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Birman, Joan S. 1927- Braids, links, and mapping class groups Annals of Mathematics Studies Braid theory Knot theory Representations of groups Kette Mathematik (DE-588)4163681-8 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Knoten Mathematik (DE-588)4164314-8 gnd Zopf Mathematik (DE-588)4191043-6 gnd Gruppentheorie (DE-588)4072157-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4163681-8 (DE-588)4022379-6 (DE-588)4164314-8 (DE-588)4191043-6 (DE-588)4072157-7 (DE-588)4148816-7 |
| title | Braids, links, and mapping class groups |
| title_auth | Braids, links, and mapping class groups |
| title_exact_search | Braids, links, and mapping class groups |
| title_full | Braids, links, and mapping class groups Joan S. Birman |
| title_fullStr | Braids, links, and mapping class groups Joan S. Birman |
| title_full_unstemmed | Braids, links, and mapping class groups Joan S. Birman |
| title_short | Braids, links, and mapping class groups |
| title_sort | braids links and mapping class groups |
| topic | Braid theory Knot theory Representations of groups Kette Mathematik (DE-588)4163681-8 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Knoten Mathematik (DE-588)4164314-8 gnd Zopf Mathematik (DE-588)4191043-6 gnd Gruppentheorie (DE-588)4072157-7 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Braid theory Knot theory Representations of groups Kette Mathematik Gruppe Mathematik Knoten Mathematik Zopf Mathematik Gruppentheorie Darstellungstheorie |
| url | https://doi.org/10.1515/9781400881420?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT birmanjoans braidslinksandmappingclassgroups |