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Book Lectures At Knots  96

Download or read book Lectures At Knots 96 written by S Suzuki and published by World Scientific. This book was released on 1997-07-04 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of ten lectures given at an international workshop/conference on knot theory held in July 1996 at Waseda University Conference Center. It was organised by the International Research Institute of Mathematical Society of Japan. The workshop was attended by nearly 170 mathematicians from Japan and 14 other countries, most of whom were specialists in knot theory. The lectures can serve as an introduction to the field for advanced undergraduates, graduates and also researchers working in areas such as theoretical physics.

Book Knots  96  Proceedings Of The Fifth International Research Institute Of Mathematical Society Of Japan

Download or read book Knots 96 Proceedings Of The Fifth International Research Institute Of Mathematical Society Of Japan written by S Suzuki and published by World Scientific. This book was released on 1997-04-19 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of an international conference on knot theory held in July 1996 at Waseda University Conference Center. It was organised by the International Research Institute of Mathematical Society of Japan. The conference was attended by nearly 180 mathematicians from Japan and 14 other countries. Most of them were specialists in knot theory. The volume contains 43 papers, which deal with significant current research in knot theory, low-dimensional topology and related topics.The volume includes papers by the following invited speakers: G Burde, R Fenn, L H Kauffman, J Levine, J M Montesinos(-A), H R Morton, K Murasugi, T Soma, and D W Sumners.

Book Lectures at Knots  96

Download or read book Lectures at Knots 96 written by S. Suzuki and published by World Scientific. This book was released on 1997 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of ten lectures given at an international workshop/conference on knot theory held in July 1996 at Waseda University Conference Center. It was organised by the International Research Institute of Mathematical Society of Japan. The workshop was attended by nearly 170 mathematicians from Japan and 14 other countries, most of whom were specialists in knot theory. The lectures can serve as an introduction to the field for advanced undergraduates, graduates and also researchers working in areas such as theoretical physics.

Book Physical Knots  Knotting  Linking  and Folding Geometric Objects in   mathbb  R  3

Download or read book Physical Knots Knotting Linking and Folding Geometric Objects in mathbb R 3 written by Jorge Alberto Calvo and published by American Mathematical Soc.. This book was released on 2002 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The properties of knotted and linked configurations in space have long been of interest to physicists and mathematicians. More recently and more widely, they have become important to biologists, chemists, computer scientists, and engineers. The depth and breadth of their applications are widely appreciated. Nevertheless, fundamental and challenging questions remain to be answered. Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volumediscusses critical questions and introduces new ideas that will stimulate multi-disciplinary applications. Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others deal with applications of mathematics to theoretical computer science, engineering,physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti. This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.

Book Braid and Knot Theory in Dimension Four

Download or read book Braid and Knot Theory in Dimension Four written by Seiichi Kamada and published by American Mathematical Soc.. This book was released on 2002 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Braid theory and knot theory are related via two famous results due to Alexander and Markov. Alexander's theorem states that any knot or link can be put into braid form. Markov's theorem gives necessary and sufficient conditions to conclude that two braids represent the same knot or link. Thus, one can use braid theory to study knot theory and vice versa. In this book, the author generalizes braid theory to dimension four. He develops the theory of surface braids and applies it tostudy surface links. In particular, the generalized Alexander and Markov theorems in dimension four are given. This book is the first to contain a complete proof of the generalized Markov theorem. Surface links are studied via the motion picture method, and some important techniques of this method arestudied. For surface braids, various methods to describe them are introduced and developed: the motion picture method, the chart description, the braid monodromy, and the braid system. These tools are fundamental to understanding and computing invariants of surface braids and surface links. Included is a table of knotted surfaces with a computation of Alexander polynomials. Braid techniques are extended to represent link homotopy classes. The book is geared toward a wide audience, from graduatestudents to specialists. It would make a suitable text for a graduate course and a valuable resource for researchers.

Book Quantum Invariants  A Study Of Knots  3 manifolds  And Their Sets

Download or read book Quantum Invariants A Study Of Knots 3 manifolds And Their Sets written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2001-12-21 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The Chern-Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants.

Book Ideal Knots

    Book Details:
  • Author : A. Stasiak
  • Publisher : World Scientific
  • Release : 1998
  • ISBN : 981279607X
  • Pages : 426 pages

Download or read book Ideal Knots written by A. Stasiak and published by World Scientific. This book was released on 1998 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 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.

Book Topology and Geometry in Polymer Science

Download or read book Topology and Geometry in Polymer Science written by Stuart G. Whittington and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications TOPOLOGY AND GEOMETRY IN POLYMER SCIENCE is based on the proceedings of a very successful one-week workshop with the same title. This workshop was an integral part of the 1995-1996 IMA program on "Mathematical Methods in Materials Science." We would like to thank Stuart G. Whittington, De Witt Sumners, and Timothy Lodge for their excellent work as organizers of the meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE This book is the product of a workshop on Topology and Geometry of Polymers, held at the IMA in June 1996. The workshop brought together topologists, combinatorialists, theoretical physicists and polymer scientists, who share an interest in characterizing and predicting the microscopic en tanglement properties of polymers, and their effect on macroscopic physical properties.

Book Energy of Knots and Conformal Geometry

Download or read book Energy of Knots and Conformal Geometry written by Jun O'Hara and published by World Scientific. This book was released on 2003 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy of knots is a theory that was introduced to create a OC canonical configurationOCO of a knot OCo 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 OC canonical configurationOCO 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. Contents: In Search of the OC Optimal EmbeddingOCO of a Knot: -Energy Functional E (); On E (2); L p Norm Energy with Higher Index; Numerical Experiments; Stereo Pictures of E (2) Minimizers; Energy of Knots in a Riemannian Manifold; Physical Knot Energies; Energy of Knots from a Conformal Geometric Viewpoint: Preparation from Conformal Geometry; The Space of Non-Trivial Spheres of a Knot; The Infinitesimal Cross Ratio; The Conformal Sin Energy E sin (c) Measure of Non-Trivial Spheres; Appendices: Generalization of the Gauss Formula for the Linking Number; The 3-Tuple Map to the Set of Circles in S 3; Conformal Moduli of a Solid Torus; Kirchhoff Elastica; Open Problems and Dreams. Readership: Graduate students and researchers in geometry & topology and numerical & computational mathematics."

Book Knot Theory and Its Applications

Download or read book Knot Theory and Its Applications written by Krishnendu Gongopadhyay and published by American Mathematical Soc.. This book was released on 2016-09-21 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the ICTS program Knot Theory and Its Applications (KTH-2013), held from December 10–20, 2013, at IISER Mohali, India. The meeting focused on the broad area of knot theory and its interaction with other disciplines of theoretical science. The program was divided into two parts. The first part was a week-long advanced school which consisted of minicourses. The second part was a discussion meeting that was meant to connect the school to the modern research areas. This volume consists of lecture notes on the topics of the advanced school, as well as surveys and research papers on current topics that connect the lecture notes with cutting-edge research in the broad area of knot theory.

Book Virtual Knots

    Book Details:
  • Author : Vasiliĭ Olegovich Manturov
  • Publisher : World Scientific
  • Release : 2012
  • ISBN : 9814401129
  • Pages : 553 pages

Download or read book Virtual Knots written by Vasiliĭ Olegovich Manturov and published by World Scientific. This book was released on 2012 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Surfaces in 4 Space

    Book Details:
  • Author : Scott Carter
  • Publisher : Springer Science & Business Media
  • Release : 2013-06-29
  • ISBN : 3662101629
  • Pages : 220 pages

Download or read book Surfaces in 4 Space written by Scott Carter and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory are presented. The last chapter comprises many recent results, and techniques for computation are presented. New tables of quandles with a few elements and the homology groups thereof are included. This book contains many new illustrations of knotted surface diagrams. The reader of the book will become intimately aware of the subtleties in going from the classical case of knotted circles in 3-space to this higher dimensional case. As a survey, the book is a guide book to the extensive literature on knotted surfaces and will become a useful reference for graduate students and researchers in mathematics and physics.

Book Knots and Physics

    Book Details:
  • Author : Louis H. Kauffman
  • Publisher : World Scientific
  • Release : 2013
  • ISBN : 9814383007
  • Pages : 865 pages

Download or read book Knots and Physics written by Louis H. Kauffman and published by World Scientific. This book was released on 2013 with total page 865 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book The Mystery of Knots

    Book Details:
  • Author : Charilaos N. Aneziris
  • Publisher : World Scientific
  • Release : 1999
  • ISBN : 9810238789
  • Pages : 410 pages

Download or read book The Mystery of Knots written by Charilaos N. Aneziris and published by World Scientific. This book was released on 1999 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most significant unsolved problems in mathematics is the complete classification of knots. The main purpose of this book is to introduce the reader to the use of computer programming to obtain the table of knots. The author presents this problem as clearly and methodically as possible, starting from the very basics. Mathematical ideas and concepts are extensively discussed, and no advanced background is required.

Book Physical and Numerical Models in Knot Theory

Download or read book Physical and Numerical Models in Knot Theory written by Jorge Alberto Calvo and published by World Scientific. This book was released on 2005 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year.This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. 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. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory.

Book Mystery Of Knots  The  Computer Programming For Knot Tabulation

Download or read book Mystery Of Knots The Computer Programming For Knot Tabulation written by Charilaos N Aneziris and published by World Scientific. This book was released on 1999-12-13 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most significant unsolved problems in mathematics is the complete classification of knots. The main purpose of this book is to introduce the reader to the use of computer programming to obtain the table of knots. The author presents this problem as clearly and methodically as possible, starting from the very basics. Mathematical ideas and concepts are extensively discussed, and no advanced background is required.

Book Fundamental Physics At The Vigier Centenary   L heretique De La Physique  Lives On

Download or read book Fundamental Physics At The Vigier Centenary L heretique De La Physique Lives On written by Richard L Amoroso and published by World Scientific. This book was released on 2021-08-27 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has not been a scientific revolution for about 100 years. One seems imminent, as QED has recently been violated at the Sigma-6 level. Kuhn, in 'The Structure of Scientific Revolutions', used Wittgenstein's famous duck-rabbit optical illusion to demonstrate how bias in interpretation causes scientists to see the same information in radically different manners, which is likely to have delayed the pending paradigm shift. Jean-Pierre Vigier, continually labeled l'hérétique de la physique and l'eternel resistant in French media, remains a pillar of modern mathematical physics. 'Heretical' works of Vigier related to extended electromagnetic theory incorporating photon mass and a longitudinal B(3) EM field, gravity, quantum theory, large-scale additional dimensions, the Dirac polarized vacuum and many more related issues are deemed by his followers to be essential to the evolution of physics. The phrase 'Lives On' was chosen in the title of this volume to claim ignored portions of his work are relevant to implementing the Paradigm Shift to an Einsteinian Unified Field Theory. Specifically, chapters about the Dirac Hypertube, Tight-Bound States and Spacetime programming provide required insights into crossing the dimensional barrier and 'proving' parts of M-Theoretic dimensionality. As happens periodically in the history of science, we live in a climate where coloring outside-the-box can have severe myopic consequences such as difficulties in passing PhD exams, challenges in grant approval or problems in receiving tenure. Since there is no conflict with Gauge Theory, once realized, many chapters in this important volume will aid in facilitating progress in physics beyond the Standard Model.