Kauffman, Louis H. 1945Overview
Publication Timeline
Most widely held works by
Louis H Kauffman
Knots and physics
by Louis H Kauffman
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54 editions published between 1991 and 2013 in English and held by 2,169 WorldCat member libraries worldwide This invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasiphysical process. The demands of knot theory, coupled with a quantumstatistical 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 third edition, a paper by the author entitled "Knot Theory and Functional Integration" 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
Hypercomplex iterations distance estimation and higher dimensional fractals
by Yumei Dang
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14 editions published between 1998 and 2002 in English and held by 943 WorldCat member libraries worldwide This book is based on the authors' research on rendering images of higher dimensional fractals by a distance estimation technique. It is selfcontained, giving a careful treatment of both the known techniques and the authors' new methods. The distance estimation technique was originally applied to Julia sets and the Mandelbrot set in the complex plane. It was justified, through the work of Douady and Hubbard, by deep results in complex analysis. In this book, the authors generalise the distance estimation to quaternionic and other higher dimensional fractals, including fractals derived from iteration in the Cayley numbers (octonionic fractals). The generalization is justified by new geometric arguments that circumvent the need for complex analysis. This puts on a firm footing the authors' present work and the second author's earlier work with John Hart and Dan Sandin. The results of this book will be of great interest to mathematicians and computer scientists interested in fractals and computer graphics
Bios a study of creation
by Hector C Sabelli
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8 editions published in 2005 in English and held by 798 WorldCat member libraries worldwide This book focuses on a prototype of creative causal processes termed BIOS and how the concept can be applied to the physical world, in medicine and in social science. This book presents methods for identifying creative features in empirical data; studies showing biotic patterns in physical, biological, and economic processes; mathematical models of bipolar (positive and negative) feedback that generate biotic patterns. These studies support the hypothesis that natural processes are creative (not determined) and causal (not random) and that bipolar feedback plays a major role in their evolution
On knots
by Louis H Kauffman
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10 editions published in 1987 in English and Undetermined and held by 635 WorldCat member libraries worldwide
Formal knot theory
by Louis H Kauffman
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16 editions published between 1983 and 2006 in English and Undetermined and held by 466 WorldCat member libraries worldwide
Introductory lectures on knot theory selected lectures presented at the Advanced School and Conference on Knot Theory and Its Applications to Physics and Biology, ICTP, Trieste, Italy, 11  29 May 2009
by Advanced School and Conference on Knot Theory and its Applications to Physics and Biology
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6 editions published between 2011 and 2012 in English and held by 460 WorldCat member libraries worldwide This volume consists primarily of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference. Knot theory is a very special topological subject: the classification of embeddings of a circle or collection of circles into threedimensional space. This is a classical topological problem and a special case of the general placement problem: Understanding the embeddings of a space X in another space Y. There have been exciting new developments in the area of knot theory and 3manifold topology in the last 25 years. From the Jones, Homflypt and Kauffman polynomials, quantum invariants of 3manifolds, through, Vassiliev invariants, topological quantum field theories, to relations with gauge theory type invariants in 4dimensional topology. More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed HeegaardFloer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with fourdimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book. It is a remarkable fact that knot theory, while very special in its problematic form, involves ideas and techniques that involve and inform much of mathematics and theoretical physics. The subject has significant applications and relations with biology, physics, combinatorics, algebra and the theory of computation. The summer school on which this book is based contained excellent lectures on the many aspects of applications of knot theory. This book gives an indepth survey of the state of the art of present day knot theory and its applications
Knots And Physics (Third Edition)
by Louis H Kauffman
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1 edition published in 2001 in English and held by 383 WorldCat member libraries worldwide This invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasiphysical process. The demands of knot theory, coupled with a quantumstatistical 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
TemperleyLieb recoupling theory and invariants of 3manifolds
by Louis H Kauffman
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7 editions published in 1994 in English and held by 339 WorldCat member libraries worldwide
The interface of knots and physics : American Mathematical Society short course, January 23, 1995, San Francisco, California
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8 editions published in 1996 in English and held by 320 WorldCat member libraries worldwide
Mathematics of quantum computation and quantum technology
by Goong Chen
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15 editions published between 2007 and 2008 in English and held by 220 WorldCat member libraries worldwide Emphasizing the mathematical methodology of quantum computing, this book presents the developments in the field. It covers quantum algorithms, quantum error correction codes, quantum teleportation, topological quantum computing, quantum search, and quantum computational technology
Quantum topology
by Louis H Kauffman
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11 editions published between 1993 and 1995 in English and held by 189 WorldCat member libraries worldwide
Hopf algebras and generalizations : AMS Special Session on Hopf Algebras at the Crossroads of Algebra, Category Theory, and Topology, October 2324, 2004, Evanston, Illinois
by Category Theory, and Topology AMS Special Session on Hopf Algebras at the Crossroads of Algebra
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9 editions published in 2007 in English and held by 188 WorldCat member libraries worldwide
Ideal knots
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6 editions published in 1998 in English and held by 178 WorldCat member libraries worldwide
Knots and applications
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8 editions published between 1994 and 1995 in English and held by 173 WorldCat member libraries worldwide
Mereon matrix unity, perspective and paradox
by Lynnclaire Dennis
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6 editions published in 2013 in English and held by 172 WorldCat member libraries worldwide Mereon is an approach to the unification of knowledge that relies on whole systems modelling. It is a scientific framework that charts the sequential, emergent growth process of systems. A dynamic structure, Mereon provides insight and a new approach to General Systems Theory and nonlinear science. Mereon evolved through a new approach to polyhedral geometry and topology that is related to the dynamics of the polyhedra. It is related to a large number of systems, physical, mathematical, and philosophical. In linking these systems, Mereon provides access to new relationships among them and combines geometric and process thinking. This book provides the fundamentals of such connections for an ongoing search for order, directionality, and diversity that is found in this unity. It is written in clear language that manages to connect diverse disciplines and in doing so, makes a complex system easily accessible and understandable. It will be of interest to mathematicians, geneticists, and all those interested in researching unity in science and astrobiology. Elaborates on several important aspects of General Systems Theory including nonlinearity.Each chapter is selfcontained and explained relative to Mereon, providing references to scientific findings that are congruent with or expanded by Mereon.Offers a new way of modelling that can be applied across the sciences
Lectures on topological fluid mechanics lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 210, 2001
by Mitchell Anthony Berger
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4 editions published in 2009 in English and held by 47 WorldCat member libraries worldwide
Knoten : Diagramme, Zustandsmodelle, Polynominvarianten
by Louis H Kauffman
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2 editions published in 1995 in German and held by 45 WorldCat member libraries worldwide
Lectures on Topological Fluid Mechanics
by De Witt Sumners
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2 editions published in 2009 in English and held by 29 WorldCat member libraries worldwide
The interface of knots and physics : an AMS short course on knots and physics
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2 editions published between 1995 and 1996 in English and held by 16 WorldCat member libraries worldwide
A Categorical Model for the Virtual Braid Group
by Louis H Kauffman
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1 edition published in 2011 in German and held by 15 WorldCat member libraries worldwide more
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Associated Subjects
Braid theory Creation CreationPhilosophy Differentiable dynamical systems Differential equations, Partial Fluid mechanics Fractals Hopf algebras Invariants Iterative methods (Mathematics) Knot polynomials Knot theory Magnetohydrodynamics Mandelbrot sets Mathematical physics Physics Quantum theory Quantum theoryMathematics Quaternions Singularities (Mathematics) System analysis System theory Thermodynamics Threemanifolds (Topology) Topology

Alternative Names
Kauffman, L. H.
Kauffman, L. H. (Louis H.), 1945
Kauffman, Louis.
Kauffman, Louis 1945
Kauffman, Louis Hirsch 1945
カウフマン, L. H
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