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.
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.
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.
Download or read book One cocycles And Knot Invariants written by Thomas Fiedler and published by World Scientific. This book was released on 2023-01-04 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: One-Cocycles and Knot Invariants is about classical knots, i.e., smooth oriented knots in 3-space. It introduces discrete combinatorial analysis in knot theory in order to solve a global tetrahedron equation. This new technique is then used to construct combinatorial 1-cocycles in a certain moduli space of knot diagrams. The construction of the moduli space makes use of the meridian and the longitude of the knot. The combinatorial 1-cocycles are therefore lifts of the well-known Conway polynomial of knots, and they can be calculated in polynomial time. The 1-cocycles can distinguish loops consisting of knot diagrams in the moduli space up to homology. They give knot invariants when they are evaluated on canonical loops in the connected components of the moduli space. They are a first candidate for numerical knot invariants which can perhaps distinguish the orientation of knots.
Download or read book Functorial Knot Theory Categories Of Tangles Coherence Categorical Deformations And Topological Invariants written by David N Yetter and published by World Scientific. This book was released on 2001-04-16 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory.This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations.
Download or read book Low Dimensional Topology written by Hanna Nencka and published by American Mathematical Soc.. This book was released on 1999 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book has two main parts. The first is devoted to the Poincare conjecture, characterizations of PL-manifolds, covering quadratic forms of links and to categories in low dimensional topology that appear in connection with conformal and quantum field theory.
Download or read book Open Problems in Mathematics written by John Forbes Nash, Jr. and published by Springer. This book was released on 2016-07-05 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.
Download or read book Quantum Invariants written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2002 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.
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.
Download or read book Knots in Hellas 98 written by C. McA. Gordon and published by World Scientific. This book was released on 2000 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been exciting developments in the area of knot theory in recent years. They include Thurston's work on geometric structures on 3-manifolds (e.g. knot complements), Gordon?Luecke work on surgeries on knots, Jones' work on invariants of links in S3, and advances in the theory of invariants of 3-manifolds based on Jones- and Vassiliev-type invariants of links. Jones ideas and Thurston's idea are connected by the following path: hyperbolic structures, PSL(2, C) representations, character varieties, quantization of the coordinate ring of the variety to skein modules (i.e. Kauffman, bracket skein module), and finally quantum invariants of 3-manifolds. This proceedings volume covers all those exciting topics.
Download or read book LinKnot written by Slavik V. Jablan and published by World Scientific. This book was released on 2007 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: LinKnot OCo 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 (available online at http: //math.ict.edu.rs ) 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, fullerens, self-referential systems, and KL automata. Sample Chapter(s). 1.1 Basic graph theory (176 KB). Contents: Notation of Knots and Links; Recognition and Generation of Knots and Links; History of Knot Theory and Applications of Knots and Links. Readership: Researchers interested in knot theory and users of Mathematica."
Download or read book Algebraic Invariants of Links written by Jonathan Arthur Hillman and published by World Scientific. This book was released on 2012 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes the features of the multicomponent case not normally considered by knot-theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, the fact that links are not usually boundary links, free coverings of homology boundary links, the lower central series as a source of invariants, nilpotent completion and algebraic closure of the link group, and disc links. Invariants of the types considered here play an essential role in many applications of knot theory to other areas of topology. This second edition introduces two new chapters OCo twisted polynomial invariants and singularities of plane curves. Each replaces brief sketches in the first edition. Chapter 2 has been reorganized, and new material has been added to four other chapters.
Download or read book Woods Hole Mathematics written by Nils Tongring and published by World Scientific. This book was released on 2004 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this volume is the contemporary mathematics of geometry and physics, but the work also discusses the problem of the secondary structure of proteins, and an overview of arc complexes with proposed applications to macromolecular folding is given.?Woods Hole has played such a vital role in both my mathematical and personal life that it is a great pleasure to see the mathematical tradition of the 1964 meeting resurrected forty years later and, as this volume shows, resurrected with new vigor and hopefully on a regular basis. I therefore consider it a signal honor to have been asked to introduce this volume with a few reminiscences of that meeting forty years ago.? Introduction by R Bott (Wolf Prize Winner, 2000).
Download or read book Mindsteps To The Cosmos written by Gerald S Hawkins and published by World Scientific. This book was released on 2002-09-10 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mindsteps to the Cosmos shows how modern global civilization depends on giant leaps of understanding that have been made in the past. Science and technology have been inspired and formulated by the sky — the cosmos in which we live. Human development could not have taken place on a cloud-shrouded planet. Mathematics was invented to track the movements of the sun, moon and stars even though back then these were thought to be gods. The space program has taken us beyond the earth, and satellite systems are exploring to the ends of the visible universe. This book provides the reader with algorithms to construct personal computer programs for finding the position of the moon and planets, and for calculating dates through historic periods in the Egyptian as well as the old and new style calendars.
Download or read book Board Games Throughout The History And Multidimensional Spaces written by Jorma Kyppo and published by World Scientific. This book was released on 2019-07-08 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this richly illustrated book, Dr Jorma Kyppö explores the history of board games dating back to Ancient Egypt, Mesopotamia, India and China. He provides a description of the evolution and various interpretations of chess. Furthermore, the book offers the study of the old Celtic and Viking board games and the old Hawaiian board game Konane, as well as a new hypothesis about the interpretation of the famous Cretan Phaistos Disk. Descriptions of several chess variations, including some highlights of the game theory and tiling in different dimensions, are followed by a multidimensional symmetrical n-person strategy game model, based on chess. Final chapter (Concluding remarks) offers the new generalizations of the Euler-Poincare's Characteristic, Pi and Fibonacci sequence.
Download or read book The Self evolving Cosmos written by Steven M. Rosen and published by World Scientific. This book was released on 2008 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book offers an original way of thinking about two of the most significant problems confronting modern theoretical physics: the unification of the forces of nature and the evolution of the universe. In bringing out the inadequacies of the prevailing approach to these questions, the author demonstrates the need for more than just a new theory. The meanings of space and time themselves must be radically rethought, which requires a whole new philosophical foundation. To this end, the book turns to the phenomenological writings of Maurice Merleau-Ponty and Martin Heidegger. Their insights into space and time bring the natural world to life in a manner well-suited to the dynamic phenomena of contemporary physics.In aligning continental thought with problems in physics and cosmology, the book makes use of topology. Phenomenological intuitions about space and time are systematically fleshed out via an unconventional and innovative approach to this qualitative branch of mathematics. The author's pioneering work in topological phenomenology is applied to such topics as quantum gravity, cosmogony, symmetry, spin, vorticity, dimension theory, Kaluza-Klein and string theories, fermion-boson interrelatedness, hypernumbers, and the mind-matter interface.
Download or read book Topological Library Part 3 Spectral Sequences In Topology written by Serguei Petrovich Novikov and published by World Scientific. This book was released on 2012-07-25 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s-1960s. The partition of these papers among the volumes is rather conditional. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated “singular homologies of fiber spaces.”
