Temperley Lieb Recoupling Theory And Invariants Of 3 Manifolds

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Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134

Louis H. Kauffman,Sostenes Lins
Temperley Lieb Recoupling Theory and Invariants of 3 Manifolds AM 134 Volume 134 Book PDF

Author : Louis H. Kauffman,Sostenes Lins
Publisher : Princeton University Press
Page : 312 pages
File Size : 49,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882533

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Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 by Louis H. Kauffman,Sostenes Lins Pdf

This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.

Temperley-Lieb Recoupling Theory and Invariants of 3-manifolds

Louis H. Kauffman,Sóstenes L. Lins,Sóstenes Lins
Temperley Lieb Recoupling Theory and Invariants of 3 manifolds Book PDF

Author : Louis H. Kauffman,Sóstenes L. Lins,Sóstenes Lins
Publisher : Unknown
Page : 296 pages
File Size : 54,6 Mb
Release : 1994
Category : Mathematics
ISBN : 0691036411

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Temperley-Lieb Recoupling Theory and Invariants of 3-manifolds by Louis H. Kauffman,Sóstenes L. Lins,Sóstenes Lins Pdf

This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.

Quantum Invariants of Knots and 3-Manifolds

Vladimir G. Turaev
Quantum Invariants of Knots and 3 Manifolds Book PDF

Author : Vladimir G. Turaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 600 pages
File Size : 54,6 Mb
Release : 2020-03-23
Category : Mathematics
ISBN : 9783110883275

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Quantum Invariants of Knots and 3-Manifolds by Vladimir G. Turaev Pdf

This monograph provides a systematic treatment of topological quantum field theories (TQFT's) in three dimensions, inspired by the discovery of the Jones polynomial of knots, the Witten-Chern-Simons field theory, and the theory of quantum groups. The author, one of the leading experts in the subject, gives a rigorous and self-contained exposition of new fundamental algebraic and topological concepts that emerged in this theory. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFT's and 2-dimensional modular functors from so-called modular categories. This gives new knot and 3-manifold invariants as well as linear representations of the mapping class groups of surfaces. In Part II the machinery of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFT's constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and Kauffman's skein modules. This book is accessible to graduate students in mathematics and physics with a knowledge of basic algebra and topology. It will be an indispensable source for everyone who wishes to enter the forefront of this rapidly growing and fascinating area at the borderline of mathematics and physics. Most of the results and techniques presented here appear in book form for the first time.

Braid Group, Knot Theory and Statistical Mechanics II

C N Yang,M L Ge
Braid Group Knot Theory and Statistical Mechanics II Book PDF

Author : C N Yang,M L Ge
Publisher : World Scientific
Page : 480 pages
File Size : 44,5 Mb
Release : 1994-02-24
Category : Science
ISBN : 9789814502788

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Braid Group, Knot Theory and Statistical Mechanics II by C N Yang,M L Ge Pdf

The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on the 1989 volume but has new material included and new contributors. Contents:On the Combinatorics of Vassiliev Invariants (J S Birman)Solvable Methods, Link Invariants and Their Applications to Physics (T Deguchi & M Wadati)Quantum Symmetry in Conformal Field Theory by Hamiltonian Methods (L D Faddeev)Yang-Baxterization & Algebraic Structures (M L Ge, K Xue, Y S Wu)Spin Networks, Topology and Discrete Physics (L H Kauffman)Tunnel Numbers of Knots and Jones-Witten Invariants (T Kohno)Knot Invariants and Statistical Mechanics: A Physicist's Perspective (F Y Wu)and other papers Readership: Mathematical physicists. keywords:Braid Group;Knot Theory;Statistical Mechanics “It has been four years since the publication in 1989 of the previous volume bearing the same title as the present one. Enormous amounts of work have been done in the meantime. We hope the present volume will provide a summary of some of these works which are still progressing in several directions.” from the foreword by C N Yang

Branched Standard Spines of 3-manifolds

Riccardo Benedetti,Carlo Petronio
Branched Standard Spines of 3 manifolds Book PDF

Author : Riccardo Benedetti,Carlo Petronio
Publisher : Springer
Page : 140 pages
File Size : 48,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540683452

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Branched Standard Spines of 3-manifolds by Riccardo Benedetti,Carlo Petronio Pdf

This book provides a unified combinatorial realization of the categroies of (closed, oriented) 3-manifolds, combed 3-manifolds, framed 3-manifolds and spin 3-manifolds. In all four cases the objects of the realization are finite enhanced graphs, and only finitely many local moves have to be taken into account. These realizations are based on the notion of branched standard spine, introduced in the book as a combination of the notion of branched surface with that of standard spine. The book is intended for readers interested in low-dimensional topology, and some familiarity with the basics is assumed. A list of questions, some of which concerning relations with the theory of quantum invariants, is enclosed.

Low-Dimensional Topology and Quantum Field Theory

Hugh Osborn
Low Dimensional Topology and Quantum Field Theory Book PDF

Author : Hugh Osborn
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 52,6 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781489916129

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Low-Dimensional Topology and Quantum Field Theory by Hugh Osborn Pdf

The motivations, goals and general culture of theoretical physics and mathematics are different. Most practitioners of either discipline have no necessity for most of the time to keep abreast of the latest developments in the other. However on occasion newly developed mathematical concepts become relevant in theoretical physics and the less rigorous theoretical physics framework may prove valuable in understanding and suggesting new theorems and approaches in pure mathematics. Such interdis ciplinary successes invariably cause much rejoicing, as over a prodigal son returned. In recent years the framework provided by quantum field theory and functional in tegrals, developed over half a century in theoretical physics, have proved a fertile soil for developments in low dimensional topology and especially knot theory. Given this background it was particularly pleasing that NATO was able to generously sup port an Advanced Research Workshop to be held in Cambridge, England from 6th to 12th September 1992 with the title Low Dimensional Topology and Quantum Field Theory. Although independently organised this overlapped as far as some speak ers were concerned with a longer term programme with the same title organised by Professor M Green, Professor E Corrigan and Dr R Lickorish. The contents of this proceedings of the workshop demonstrate the breadth of topics now of interest on the interface between theoretical physics and mathematics as well as the sophistication of the mathematical tools required in current theoretical physics.

Geometry and Physics

H. Pedersen,J. Andersen,J. Dupont,Andrew Swann
Geometry and Physics Book PDF

Author : H. Pedersen,J. Andersen,J. Dupont,Andrew Swann
Publisher : CRC Press
Page : 772 pages
File Size : 51,6 Mb
Release : 1996-10-11
Category : Mathematics
ISBN : 0824797914

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Geometry and Physics by H. Pedersen,J. Andersen,J. Dupont,Andrew Swann Pdf

"Based on the proceedings of the Special Session on Geometry and Physics held over a six month period at the University of Aarhus, Denmark and on articles from the Summer school held at Odense University, Denmark. Offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts."

Knots and Physics

Louis H Kauffman
Knots and Physics Book PDF

Author : Louis H Kauffman
Publisher : World Scientific
Page : 740 pages
File Size : 49,7 Mb
Release : 1994-01-15
Category : Science
ISBN : 9789814502375

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Knots and Physics by Louis H Kauffman Pdf

In this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included. This book is an introduction to knot and link invariants as generalized amplitudes (vacuum–vacuum 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 has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems. Contents:Physical KnotsStates and the Bracket PolynomialThe Jones Polynomial and Its GeneralizationsBraids and the Jones PolynomialFormal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)qYang-Baxter Models for Specializations of the Homfly PolynomialThe Alexander PolynomialKnot-Crystals — Classical Knot Theory in Modern GuiseThe Kauffman PolynomialThree Manifold Invariants from the Jones PolynomialIntegral Heuristics and Witten' s InvariantsThe Chromatic PolynomialThe Potts Model and the Dichromatic PolynomialThe Penrose Theory of Spin NetworksKnots and Strings — Knotted StringsDNA and Quantum Field TheoryKnots in Dynamical Systems — The Lorenz Attractorand other papers Readership: Physicists, mathematical physicists and mathematicians. keywords: Reviews of the First Edition: “It is an attractive book for physicists with profuse and often entertaining illustrations … proofs … seldom heavy and nearly always well explained with pictures… succeeds in infusing his own excitement and enthusiasm for these discoveries and their potential implications.” Physics Today “… here is a gold mine where, with care and patience, one should get acquainted with a beautiful subject under the guidance of a most original and imaginative mind.” Mathematical Reviews

Knots and Physics

Louis H. Kauffman
Knots and Physics Book PDF

Author : Louis H. Kauffman
Publisher : World Scientific
Page : 865 pages
File Size : 52,8 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814383004

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Knots and Physics by Louis H. Kauffman Pdf

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.

Functional Integration

Cécile Dewitt-Morette,Antoine Folacci
Functional Integration Book PDF

Author : Cécile Dewitt-Morette,Antoine Folacci
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 44,7 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781489903198

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Functional Integration by Cécile Dewitt-Morette,Antoine Folacci Pdf

The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.

Algorithmic Topology and Classification of 3-Manifolds

Sergei Matveev
Algorithmic Topology and Classification of 3 Manifolds Book PDF

Author : Sergei Matveev
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 45,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662051023

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Algorithmic Topology and Classification of 3-Manifolds by Sergei Matveev Pdf

Here is a thorough review of topics in 3-dimensional topology, derived from a decade of courses taught by the author. The author keeps the exposition to an elementary level by presenting the material mainly from the point of view of special polyhedra and special spines of 3-manifolds. The book culminates with the recognition procedure for Haken manifolds, and includes up-to-date results in computer enumeration of 3-mainfolds. The second edition adds new results, new proofs, and commentaries. Algorithmic Topology and Classification of 3-Manifolds serves as a standard reference for algorithmic 3-dimensional topology for both graduate students and researchers.

Advances in Topological Quantum Field Theory

John M. Bryden
Advances in Topological Quantum Field Theory Book PDF

Author : John M. Bryden
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 54,5 Mb
Release : 2007-09-27
Category : Mathematics
ISBN : 9781402027727

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Advances in Topological Quantum Field Theory by John M. Bryden Pdf

This volume is the conference proceedings of the NATO ARW during August 2001 at Kananaskis Village, Canada on 'New Techniques in Topological Quantum Field Theory'. This conference brought together specialists from a number of different fields all related to Topological Quantum Field Theory. The theme of this conference was to attempt to find new methods in quantum topology from the interaction with specialists in these other fields. The featured articles include papers by V. Vassiliev on combinatorial formulas for cohomology of spaces of Knots, the computation of Ohtsuki series by N. Jacoby and R. Lawrence, and a paper by M. Asaeda and J. Przytycki on the torsion conjecture for Khovanov homology by Shumakovitch. Moreover, there are articles on more classical topics related to manifolds and braid groups by such well known authors as D. Rolfsen, H. Zieschang and F. Cohen.

Handbook of Geometric Topology

R.B. Sher,R.J. Daverman
Handbook of Geometric Topology Book PDF

Author : R.B. Sher,R.J. Daverman
Publisher : Elsevier
Page : 1145 pages
File Size : 45,8 Mb
Release : 2001-12-20
Category : Mathematics
ISBN : 9780080532851

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Handbook of Geometric Topology by R.B. Sher,R.J. Daverman Pdf

Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.

Knot Theory and Its Applications

Krishnendu Gongopadhyay,Rama Mishra
Knot Theory and Its Applications Book PDF

Author : Krishnendu Gongopadhyay,Rama Mishra
Publisher : American Mathematical Soc.
Page : 357 pages
File Size : 40,9 Mb
Release : 2016-09-21
Category : Knot theory
ISBN : 9781470422578

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Knot Theory and Its Applications by Krishnendu Gongopadhyay,Rama Mishra Pdf

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.

Gems, Computers and Attractors For 3-Manifolds

S¢stenes Lins
Gems Computers and Attractors For 3 Manifolds Book PDF

Author : S¢stenes Lins
Publisher : World Scientific
Page : 468 pages
File Size : 54,6 Mb
Release : 1995
Category : Three-manifolds (Topology)
ISBN : 9789812796196

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Gems, Computers and Attractors For 3-Manifolds by S¢stenes Lins Pdf

This text provides a guide to dealing with 3-manifolds by computers. Its emphasis is on presenting algorithms which are used for solving (in practice) the homeomorphism problem for the smallest of these objects. The key concept is the 3-gem, a special kind of edge-colored graph, which encodes the manifold via a ball complex. Passages between 3-gems and more standard presentations like Heegaard diagrams and surgery descriptions are provided. A catalogue of all closed orientable 3-manifolds induced by 3-gems up to 30 vertices is included. In order to help the classification, various invariants are presented, including the new quantum invariants.