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Author: Renzo L. Ricca
Publisher: Springer Nature
ISBN: 3031579852
Category :
Languages : en
Pages : 355
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Book Description
Author: Renzo L. Ricca
Publisher: Springer Nature
ISBN: 3031579852
Category :
Languages : en
Pages : 355
Get Book Here
Book Description
Author: Colin Conrad Adams
Publisher: American Mathematical Soc.
ISBN: 0821836781
Category : Mathematics
Languages : en
Pages : 330
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Book Description
Knots 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.
Author: John C Baez
Publisher: World Scientific Publishing Company
ISBN: 9813103248
Category : Science
Languages : en
Pages : 481
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Book Description
This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.
Author: Dale Rolfsen
Publisher: American Mathematical Soc.
ISBN: 0821834363
Category : Mathematics
Languages : en
Pages : 458
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Book Description
Rolfsen'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.""
Author: Colin C. Adams
Publisher: Springer
ISBN: 3030160319
Category : Mathematics
Languages : en
Pages : 476
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Book Description
This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.
Author: Louis H. Kauffman
Publisher: World Scientific
ISBN: 9810241119
Category : Science
Languages : en
Pages : 788
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Book Description
This 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 a 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 third edition, a paper by the author entitled "Functional Integration and Vassiliev invariants" has been added. This paper shows how the Kontsevich integral approach to the Vassiliev invariants is directly related to the perturbative expansion of Witten's functional integral. While the book supplies the background, this paper can be read independently as an introduction to quantum field theory and knot invariants and their relation to quantum gravity. As in the second edition, there is a selection of papers by the author at the end of the book. Numerous clarifying remarks have been added to the text.
Author: Louis H Kauffman
Publisher: World Scientific
ISBN: 9814460303
Category : Mathematics
Languages : en
Pages : 865
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Book Description
This 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.
Author: Thomas Nail
Publisher: Oxford University Press
ISBN: 0190924047
Category : Art
Languages : en
Pages : 320
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Book Description
We live in an age of the mobile image. The world today is absolutely saturated with images of all kinds circulating around the world at an incredible rate. The movement of the image has never been more extraordinary than it is today. This recent kinetic revolution of the image has enormous consequences not only for the way we think about contemporary art and aesthetics but also for art history as well. Responding to this historical moment, Theory of the Image offers a fresh new theory and history of art from the perspective of this epoch-defining mobility. The image has been understood in many ways, but it is rarely understood to be fundamentally in motion. The original and materialist approach is what defines Theory of the Image and what allows it to offer the first kinetic history of the Western art tradition. In this book, Thomas Nail further develops his larger philosophy of movement into a comprehensive "kinesthetic" of the moving image from prehistory to the present. The book concludes with a vivid analysis of the contemporary digital image and its hybridity, ultimately outlining new territory for research and exploration across aesthetics, art history, cultural theory, and media studies.
Author: Clifford W. Ashley
Publisher: BoD – Books on Demand
ISBN: 3963320001
Category : Reference
Languages : en
Pages : 630
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Book Description
What 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.
Author: Thomas Nail
Publisher: Oxford University Press
ISBN: 0190908939
Category : Philosophy
Languages : en
Pages : 496
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Book Description
More than at any other time in human history, we live in an age defined by movement and mobility; and yet, we lack a unifying theory which takes this seriously as a starting point for philosophy. The history of philosophy has systematically explained movement as derived from something else that does not move: space, eternity, force, and time. Why, when movement has always been central to human societies, did a philosophy based on movement never take hold? This book finally overturns this long-standing metaphysical tradition by placing movement at the heart of philosophy. In doing so, Being and Motion provides a completely new understanding of the most fundamental categories of ontology from a movement-oriented perspective: quality, quantity, relation, modality, and others. It also provides the first history of the philosophy of motion, from early prehistoric mythologies up to contemporary ontologies. Through its systematic ontology of movement, Being and Motion provides a path-breaking historical ontology of our present.