Knotted Fields
Author: Renzo L. Ricca
Publisher: Springer Nature
Published:
Total Pages: 355
ISBN-13: 3031579852
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The Knot Book
Author: Colin Conrad Adams
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 330
ISBN-13: 0821836781
DOWNLOAD EBOOKKnots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Ideal Knots
Author: Andrzej Stasiak
Publisher: World Scientific
Published: 1998
Total Pages: 426
ISBN-13: 9810235305
DOWNLOAD EBOOKIn this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of knotted arrangements of bistable chemical systems, the trajectories of knotted solitons, and the shapes of knots which can be tied using the shortest piece of elastic rope with a constant diameter.
Knots and Applications
Author: Louis H. Kauffman
Publisher: World Scientific
Published: 1995
Total Pages: 502
ISBN-13: 9789810220044
DOWNLOAD EBOOKThis volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Thomson) on the 19th century theory of vortex atoms, reprints of modern papers on knotted flux in physics and in fluid dynamics and knotted wormholes in general relativity. It also includes papers on Witten's approach to knots via quantum field theory and applications of this approach to quantum gravity and the Ising model in three dimensions. Other papers discuss the topology of RNA folding in relation to invariants of graphs and Vassiliev invariants, the entanglement structures of polymers, the synthesis of molecular Mobius strips and knotted molecules. The book begins with an article on the applications of knot theory to the foundations of mathematics and ends with an article on topology and visual perception. This volume will be of immense interest to all workers interested in new possibilities in the uses of knots and knot theory.
Knots and Links
Author: Dale Rolfsen
Publisher: American Mathematical Soc.
Published: 2003
Total Pages: 458
ISBN-13: 0821834363
DOWNLOAD EBOOKRolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book.""
The Geometry and Physics of Knots
Author: Michael Francis Atiyah
Publisher: Cambridge University Press
Published: 1990-08-23
Total Pages: 112
ISBN-13: 9780521395540
DOWNLOAD EBOOKThese notes deal with an area that lies at the crossroads of mathematics and physics and rest primarily on the pioneering work of Vaughan Jones and Edward Witten, who related polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions.
Knots and Physics
Author: Louis H. Kauffman
Publisher: World Scientific
Published: 2001
Total Pages: 794
ISBN-13: 9789812384836
DOWNLOAD EBOOKThis invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.
Knots And Physics (Second Edition)
Author: Louis H Kauffman
Publisher: World Scientific
Published: 1994-01-15
Total Pages: 739
ISBN-13: 9814502375
DOWNLOAD EBOOKIn this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included.This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems.
Knots And Physics (Fourth Edition)
Author: Louis H Kauffman
Publisher: World Scientific
Published: 2012-11-09
Total Pages: 865
ISBN-13: 9814460303
DOWNLOAD EBOOKThis invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part II is a set of lectures on various topics related to Part I. Part II includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems.In this new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.
THE ASHLEY BOOK OF KNOTS
Author: Clifford W. Ashley
Publisher: BoD – Books on Demand
Published: 2023-06-20
Total Pages: 630
ISBN-13: 3963320001
DOWNLOAD EBOOKWhat else needs to be said about knots? Almost 650 pages of incredible knowledge, presented in a truzly unique manner. This is not a book of knots, it is the BOOK OF KNOTS. Was muss noch über Knoten gesagt werden? Fast 650 Seiten unglaubliches Wissen, präsentiert in einer wahrhaft einzigartigen Weise. Dies ist kein Buch über Knoten, es ist das BUCH DER KNOTEN.
