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Science

A Gentle Introduction To Knots, Links And Braids

A Gentle Introduction To Knots, Links And Braids PDF Author: Ruben Aldrovandi
Publisher: World Scientific
ISBN: 9811248508
Category : Science
Languages : en
Pages : 216

Book 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.

A Gentle Introduction To Knots, Links And Braids

A Gentle Introduction To Knots, Links And Braids PDF Author: Ruben Aldrovandi
Publisher: World Scientific
ISBN: 9811248508
Category : Science
Languages : en
Pages : 216

Book 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.

A Gentle Introduction to Knots, Links and Braids

A Gentle Introduction to Knots, Links and Braids PDF Author: Ruben Aldrovandi
Publisher: World Scientific Publishing Company
ISBN: 9789811249327
Category : Science
Languages : en
Pages : 216

Book 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.

Knots, Links, Braids and 3-manifolds

Knots, Links, Braids and 3-manifolds PDF Author: Viktor Vasilʹevich Prasolov
Publisher: Amer Mathematical Society
ISBN:
Category : Science
Languages : en
Pages : 239

Book Description
This book is intended for researchers working in geometry and topology.

Bulletin (new Series) of the American Mathematical Society

Bulletin (new Series) of the American Mathematical Society PDF Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages :

Book Description


Knot Theory

Knot Theory PDF Author: Vassily Manturov
Publisher: CRC Press
ISBN: 9780415310017
Category : Mathematics
Languages : en
Pages : 416

Book Description
Since discovery of the Jones polynomial, knot theory has enjoyed a virtual explosion of important results and now plays a significant role in modern mathematics. In a unique presentation with contents not found in any other monograph, Knot Theory describes, with full proofs, the main concepts and the latest investigations in the field. The book is divided into six thematic sections. The first part discusses "pre-Vassiliev" knot theory, from knot arithmetics through the Jones polynomial and the famous Kauffman-Murasugi theorem. The second part explores braid theory, including braids in different spaces and simple word recognition algorithms. A section devoted to the Vassiliev knot invariants follows, wherein the author proves that Vassiliev invariants are stronger than all polynomial invariants and introduces Bar-Natan's theory on Lie algebra respresentations and knots. The fourth part describes a new way, proposed by the author, to encode knots by d-diagrams. This method allows the encoding of topological objects by words in a finite alphabet. Part Five delves into virtual knot theory and virtualizations of knot and link invariants. This section includes the author's own important results regarding new invariants of virtual knots. The book concludes with an introduction to knots in 3-manifolds and Legendrian knots and links, including Chekanov's differential graded algebra (DGA) construction. Knot Theory is notable not only for its expert presentation of knot theory's state of the art but also for its accessibility. It is valuable as a professional reference and will serve equally well as a text for a course on knot theory.

The Illustrated London News

The Illustrated London News PDF Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :

Book Description


The Compact Edition of the Oxford English Dictionary: Complete Text Reproduced Micrographically: P-Z, Supplement and bibliography

The Compact Edition of the Oxford English Dictionary: Complete Text Reproduced Micrographically: P-Z, Supplement and bibliography PDF Author:
Publisher:
ISBN:
Category : English language
Languages : en
Pages : 4116

Book Description
Micrographic reproduction of the 13 volume Oxford English dictionary published in 1933.