The Theory Of Quantum Torus Knots Volume Iii
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The Theory Of Quantum Torus Knots Volume Iii
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Author : Michael Ungs
language : en
Publisher: Lulu.com
Release Date : 2010-08-16
The Theory Of Quantum Torus Knots Volume Iii written by Michael Ungs and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-16 with Technology & Engineering categories.
Appendicies A to I that are referenced by Volumes I and II in the theory of quantum torus knots (QTK). A detailed mathematical derivation of space curves is provided that links the diverse fields of superfluids, quantum mechanics, and hydrodynamics.
The Theory Of Quantum Torus Knots Volume Ii
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Author : Michael Ungs
language : en
Publisher: Lulu.com
Release Date : 2010-06-23
The Theory Of Quantum Torus Knots Volume Ii written by Michael Ungs and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-23 with Technology & Engineering categories.
A detailed mathematical derivation of space curves is presented that links the diverse fields of superfluids, quantum mechanics, Navier-Stokes hydrodynamics, and Maxwell electromagnetism by a common foundation. The basic mathematical building block is called the theory of quantum torus knots (QTK).
The Theory Of Quantum Torus Knots
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Author :
language : en
Publisher:
Release Date : 2020-05-06
The Theory Of Quantum Torus Knots written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-06 with categories.
The Knot Book
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Author : Colin Conrad Adams
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
The Knot Book written by Colin Conrad Adams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Volume Conjecture For Knots
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Author : Hitoshi Murakami
language : en
Publisher: Springer
Release Date : 2018-08-15
Volume Conjecture For Knots written by Hitoshi Murakami and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-15 with Science categories.
The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement. Here the colored Jones polynomial is a generalization of the celebrated Jones polynomial and is defined by using a so-called R-matrix that is associated with the N-dimensional representation of the Lie algebra sl(2;C). The volume conjecture was first stated by R. Kashaev in terms of his own invariant defined by using the quantum dilogarithm. Later H. Murakami and J. Murakami proved that Kashaev’s invariant is nothing but the N-dimensional colored Jones polynomial evaluated at the Nth root of unity. Then the volume conjecture turns out to be a conjecture that relates an algebraic object, the colored Jones polynomial, with a geometric object, the volume. In this book we start with the definition of the colored Jones polynomial by using braid presentations of knots. Then we state the volume conjecture and give a very elementary proof of the conjecture for the figure-eight knot following T. Ekholm. We then give a rough idea of the “proof”, that is, we show why we think the conjecture is true at least in the case of hyperbolic knots by showing how the summation formula for the colored Jones polynomial “looks like” the hyperbolicity equations of the knot complement. We also describe a generalization of the volume conjecture that corresponds to a deformation of the complete hyperbolic structure of a knot complement. This generalization would relate the colored Jones polynomial of a knot to the volume and the Chern–Simons invariant of a certain representation of the fundamental group of the knot complement to the Lie group SL(2;C). We finish by mentioning further generalizations of the volume conjecture.
Chern Simons Gauge Theory 20 Years After
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Author : Jørgen E. Andersen
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Chern Simons Gauge Theory 20 Years After written by Jørgen E. Andersen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory. The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.
Lectures On Geometry
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Author : Nicholas Michael John Woodhouse
language : en
Publisher: Oxford University Press
Release Date : 2017
Lectures On Geometry written by Nicholas Michael John Woodhouse and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
This book contains a series of chapters by leading researchers and practitioners on community engagement approaches in the field of counterterrorism and counterinsurgency. It presents existing and emerging community engagement models in various parts of the world which could serve as effective models for governments keen to work with community leaders to manage and reduce the terrorist threat. The book emphasizes the strength of communities as central to government approaches in countering violent extremism.
The Interaction Of Analysis And Geometry
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Author : Victor I. Burenkov
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
The Interaction Of Analysis And Geometry written by Victor I. Burenkov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Based on talks given at the International Conference on Analysis and Geometry in honor of the 75th birthday of Yurii Reshetnyak (Novosibirsk, 2004), this title includes topics such as geometry of spaces with bounded curvature in the sense of Alexandrov, quasiconformal mappings and mappings with bounded distortion, and nonlinear potential theory."
An Introduction To Quantum And Vassiliev Knot Invariants
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Author : David M. Jackson
language : en
Publisher: Springer
Release Date : 2019-05-04
An Introduction To Quantum And Vassiliev Knot Invariants written by David M. Jackson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-04 with Mathematics categories.
This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant.
Princeton Alumni Weekly
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Author :
language : en
Publisher: princeton alumni weekly
Release Date : 2009
Princeton Alumni Weekly written by and has been published by princeton alumni weekly this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.