Название: Energy of knots and conformal geometry ISBN: 9812383166 ISBN-13(EAN): 9789812383167 Издательство: World Scientific Publishing Рейтинг: Цена: 10443 р. Наличие на складе: Поставка под заказ.
Описание: Energy of knots is a theory that was introduced to create a "canonical configuration" of a knot - a beautiful knot which represents its knot type. This book
introduces several kinds of energies, and studies the problem of whether or not there is a "canonical configuration" of a knot in each knot type. It also considers this problems in the
context of conformal geometry.
The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical
knotting and unknotting through numerical experiments.
Автор: Gelca Razvan Название: Theta Functions and Knots ISBN: 9814520578 ISBN-13(EAN): 9789814520577 Издательство: World Scientific Publishing Рейтинг: Цена: 15057 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents the relationship between classical theta functions and knots. It is based on a novel idea of Răzvan Gelca and Alejandro Uribe, which converts Weil's representation of the Heisenberg group on theta functions to a knot theoretical framework, by giving a topological interpretation to a certain induced representation. It also explains how the discrete Fourier transform can be related to 3- and 4-dimensional topology.Theta Functions and Knots can be read in two perspectives. Readers with an interest in theta functions or knot theory can learn how the two are related. Those interested in Chern-Simons theory will find here an introduction using the simplest case, that of abelian Chern-Simons theory. Moreover, the construction of abelian Chern-Simons theory is based entirely on quantum mechanics and not on quantum field theory as it is usually done.Both the theory of theta functions and low dimensional topology are presented in detail, in order to underline how deep the connection between these two fundamental mathematical subjects is. Hence the book is self-contained with a unified presentation. It is suitable for an advanced graduate course, as well as for self-study.
Автор: Markus Banagl; Denis Vogel Название: The Mathematics of Knots ISBN: 3642266223 ISBN-13(EAN): 9783642266225 Издательство: Springer Рейтинг: Цена: 15427 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book offers up-to-date original research and survey articles on actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. The contents arise from the Heidelberg Knot Theory Semester of winter 2008-09.
Автор: Kauffman Louis H Название: Knots and Physics ISBN: 9814383015 ISBN-13(EAN): 9789814383011 Издательство: World Scientific Publishing Рейтинг: Цена: 9229 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Автор: Manturov Vassily Olegovich Название: Virtual Knots ISBN: 9814401129 ISBN-13(EAN): 9789814401128 Издательство: World Scientific Publishing Рейтинг: Цена: 16879 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classical) knot theory.Virtual knots were discovered by Louis Kauffman in 1996. When virtual knot theory arose, it became clear that classical knot theory was a small integral part of a larger theory, and studying properties of virtual knots helped one understand better some aspects of classical knot theory and encouraged the study of further problems. Virtual knot theory finds its applications in classical knot theory. Virtual knot theory occupies an intermediate position between the theory of knots in arbitrary three-manifold and classical knot theory.In this book we present the latest achievements in virtual knot theory including Khovanov homology theory and parity theory due to V O Manturov and graph-link theory due to both authors. By means of parity, one can construct functorial mappings from knots to knots, filtrations on the space of knots, refine many invariants and prove minimality of many series of knot diagrams.Graph-links can be treated as “diagramless knot theory”: such “links” have crossings, but they do not have arcs connecting these crossings. It turns out, however, that to graph-links one can extend many methods of classical and virtual knot theories, in particular, the Khovanov homology and the parity theory.
Автор: Morishita Название: Knots and Primes ISBN: 1447121570 ISBN-13(EAN): 9781447121572 Издательство: Springer Цена: 5142 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory. Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry. ?
Автор: Stasiak A. Название: Ideal knots ISBN: 9810235305 ISBN-13(EAN): 9789810235307 Издательство: World Scientific Publishing Рейтинг: Цена: 14571 р. Наличие на складе: Поставка под заказ.
Описание: This text discusses topics including: 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.
Автор: Banagl Название: The Mathematics of Knots ISBN: 3642156363 ISBN-13(EAN): 9783642156366 Издательство: Springer Рейтинг: Цена: 15427 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.
Описание: The physical properties of knotted and linked configurations in space have been of interest to physicists and mathematicians for a long time. More recently and
more widely, they have become interesting to biological and computer scientists, and to engineers among others. The depth of importance and breadth of application are now widely
appreciated.
In t
is volume, there are several contributions from researchers who are using computers to study problems that would otherwise be untractable. While computations have long been used to
analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. From
properties of knot invariants, to knot tabulation, studies of hyperbolic structures, knot energies, and to the exploration of spaces of knots, computers have opened the doors to problems
that would have otherwise been too difficult to do by hand computation.
There are also contributions concentrating on models that researchers use to understand knotting,
linking, and entanglement in physical and biological systems. Topics range from knotted umbilical cords, to studies of DNA knots and knots in proteins.
Автор: Slavik Jablan,Radmila Sazdanovic Название: LINKNOT: Knot Theory by Computer ISBN: 9812772235 ISBN-13(EAN): 9789812772237 Издательство: World Scientific Publishing Рейтинг: Цена: 14571 р. Наличие на складе: Поставка под заказ.
Описание: "LinKnot - Knot Theory by Computer" provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with
backgrounds in other exact sciences, including chemistry, molecular biology and physics. The book covers basic notions in knot theory, as well as new methods for handling open
problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves. Hands-on
computations using Mathematica or the webMathematica package LinKnot and beautiful illustrations facilitate better learning and understanding."LinKnot" is also a powerful research
tool for experimental mathematics implementation of Caudron's ideas.
The use of Conway notation enables experimenting with large families of knots and links. Conjectures
discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullere
s, self-referential systems, and KL automata.
Автор: Murasugi Название: Knot Theory and Its Applications ISBN: 081764718X ISBN-13(EAN): 9780817647186 Издательство: Springer Рейтинг: Цена: 3268 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Knot theory is a concept in algebraic topology that has found applications to a variety of mathematical problems as well as in computer science, biological and medical research, and mathematical physics. This book is directed to a broad audience of research workers and beginning graduate students in these fields. It contains most of the fundamental classical facts about the theory, such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials, as well as more recent developments and special topics such as chord diagrams and covering spaces. It is an introduction to the fascinating study of knots and provides insight into recent applications to such studies as DNA research and graph theory. The author clearly outlines what is known and what is not known about knots. He has been careful to avoid advanced mathematical terminology or intricate techniques in algebraic topology or group theory. There are numerous diagrams and exercises relating the material. Developments over the past ten years are described, in particular the study of Jones polynomials and the Vassiliev invariants.Each chapter includes a supplement that consists of interesting historical as well as mathematical comments. The book will be readable by senior undergraduate students as well as beginning graduate students in mathematics, computer science and modern biological, medical and physical research.
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