A Gentle Introduction to Knots, Links and Braids
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | |
Tipo de documento: | Livro |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1142/12591 http://hdl.handle.net/11449/246320 |
Resumo: | The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang–Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory. This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics. |
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A Gentle Introduction to Knots, Links and BraidsThe interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang–Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory. This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.São Paulo State University (UNESP)Federal University of ABCSão Paulo State University (UNESP)Universidade Estadual Paulista (UNESP)Federal University of ABCAldrovandi, Ruben [UNESP]da Rocha, Roldão2023-07-29T12:37:46Z2023-07-29T12:37:46Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/book1-189http://dx.doi.org/10.1142/12591A Gentle Introduction to Knots, Links and Braids, p. 1-189.http://hdl.handle.net/11449/24632010.1142/125912-s2.0-85142094608Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengA Gentle Introduction to Knots, Links and Braidsinfo:eu-repo/semantics/openAccess2023-07-29T12:37:46Zoai:repositorio.unesp.br:11449/246320Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-07-29T12:37:46Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
A Gentle Introduction to Knots, Links and Braids |
title |
A Gentle Introduction to Knots, Links and Braids |
spellingShingle |
A Gentle Introduction to Knots, Links and Braids Aldrovandi, Ruben [UNESP] |
title_short |
A Gentle Introduction to Knots, Links and Braids |
title_full |
A Gentle Introduction to Knots, Links and Braids |
title_fullStr |
A Gentle Introduction to Knots, Links and Braids |
title_full_unstemmed |
A Gentle Introduction to Knots, Links and Braids |
title_sort |
A Gentle Introduction to Knots, Links and Braids |
author |
Aldrovandi, Ruben [UNESP] |
author_facet |
Aldrovandi, Ruben [UNESP] da Rocha, Roldão |
author_role |
author |
author2 |
da Rocha, Roldão |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) Federal University of ABC |
dc.contributor.author.fl_str_mv |
Aldrovandi, Ruben [UNESP] da Rocha, Roldão |
description |
The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang–Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory. This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-01-01 2023-07-29T12:37:46Z 2023-07-29T12:37:46Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/book |
format |
book |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1142/12591 A Gentle Introduction to Knots, Links and Braids, p. 1-189. http://hdl.handle.net/11449/246320 10.1142/12591 2-s2.0-85142094608 |
url |
http://dx.doi.org/10.1142/12591 http://hdl.handle.net/11449/246320 |
identifier_str_mv |
A Gentle Introduction to Knots, Links and Braids, p. 1-189. 10.1142/12591 2-s2.0-85142094608 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
A Gentle Introduction to Knots, Links and Braids |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
1-189 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
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1803047291566686208 |