The calculus of braids: an introduction, and beyond
Everyone knows what braids are, whether they be made of hair, knitting wool, or electrical cables. However, it is not so evident that we can construct a theory about them, i.e. to elaborate a coherent and mathematically interesting corpus of results concerning them. This book demonstrates that there...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2021
|
| Schriftenreihe: | London Mathematical Society student texts
100 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Everyone knows what braids are, whether they be made of hair, knitting wool, or electrical cables. However, it is not so evident that we can construct a theory about them, i.e. to elaborate a coherent and mathematically interesting corpus of results concerning them. This book demonstrates that there is a resoundingly positive response to this question: braids are fascinating objects, with a variety of rich mathematical properties and potential applications. A special emphasis is placed on the algorithmic aspects and on what can be called the 'calculus of braids', in particular the problem of isotopy. Prerequisites are kept to a minimum, with most results being established from scratch. An appendix at the end of each chapter gives a detailed introduction to the more advanced notions required, including monoids and group presentations. Also included is a range of carefully selected exercises to help the reader test their knowledge, with solutions available |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 01 Sep 2021) Geometric braids -- Braid groups -- Braid monoids -- The greedy normal form -- The Artin representation -- Handle reduction -- The Dynnikov coordinates -- A few avenues of investigation -- Solutions to the exercises |
| Beschreibung: | 1 Online-Ressource (xii, 245 Seiten) |
| ISBN: | 9781108921121 |
| DOI: | 10.1017/9781108921121 |
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| author | Dehornoy, Patrick 1952-2019 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| illustrated | Not Illustrated |
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| isbn | 9781108921121 |
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| spelling | Dehornoy, Patrick 1952-2019 (DE-588)113599625 aut Calcul des tresses <Englisch> The calculus of braids an introduction, and beyond Patrick Dehornoy ; translated by Danièle Gibbons, Greg Gibbons Cambridge Cambridge University Press 2021 1 Online-Ressource (xii, 245 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society student texts 100 Title from publisher's bibliographic system (viewed on 01 Sep 2021) Geometric braids -- Braid groups -- Braid monoids -- The greedy normal form -- The Artin representation -- Handle reduction -- The Dynnikov coordinates -- A few avenues of investigation -- Solutions to the exercises Everyone knows what braids are, whether they be made of hair, knitting wool, or electrical cables. However, it is not so evident that we can construct a theory about them, i.e. to elaborate a coherent and mathematically interesting corpus of results concerning them. This book demonstrates that there is a resoundingly positive response to this question: braids are fascinating objects, with a variety of rich mathematical properties and potential applications. A special emphasis is placed on the algorithmic aspects and on what can be called the 'calculus of braids', in particular the problem of isotopy. Prerequisites are kept to a minimum, with most results being established from scratch. An appendix at the end of each chapter gives a detailed introduction to the more advanced notions required, including monoids and group presentations. Also included is a range of carefully selected exercises to help the reader test their knowledge, with solutions available Braid theory Zopf Mathematik (DE-588)4191043-6 gnd rswk-swf Zopf Mathematik (DE-588)4191043-6 s DE-604 Gibbons, Danièle ca. 20./21. Jh. (DE-588)1203756402 trl Gibbons, Greg ca. 20./21. Jh. (DE-588)1203756526 trl Erscheint auch als Druck-Ausgabe 978-1-108-84394-2 https://doi.org/10.1017/9781108921121 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Dehornoy, Patrick 1952-2019 The calculus of braids an introduction, and beyond Braid theory Zopf Mathematik (DE-588)4191043-6 gnd |
| subject_GND | (DE-588)4191043-6 |
| title | The calculus of braids an introduction, and beyond |
| title_alt | Calcul des tresses <Englisch> |
| title_auth | The calculus of braids an introduction, and beyond |
| title_exact_search | The calculus of braids an introduction, and beyond |
| title_exact_search_txtP | The calculus of braids an introduction, and beyond |
| title_full | The calculus of braids an introduction, and beyond Patrick Dehornoy ; translated by Danièle Gibbons, Greg Gibbons |
| title_fullStr | The calculus of braids an introduction, and beyond Patrick Dehornoy ; translated by Danièle Gibbons, Greg Gibbons |
| title_full_unstemmed | The calculus of braids an introduction, and beyond Patrick Dehornoy ; translated by Danièle Gibbons, Greg Gibbons |
| title_short | The calculus of braids |
| title_sort | the calculus of braids an introduction and beyond |
| title_sub | an introduction, and beyond |
| topic | Braid theory Zopf Mathematik (DE-588)4191043-6 gnd |
| topic_facet | Braid theory Zopf Mathematik |
| url | https://doi.org/10.1017/9781108921121 |
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