Braid And Knot Theory In Dimension Four

Braid And Knot Theory In Dimension Four Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Braid And Knot Theory In Dimension Four book. This book definitely worth reading, it is an incredibly well-written.

Braid and Knot Theory in Dimension Four

Seiichi Kamada
Braid and Knot Theory in Dimension Four Book PDF

Author : Seiichi Kamada
Publisher : American Mathematical Soc.
Page : 329 pages
File Size : 48,5 Mb
Release : 2002
Category : Braid theory
ISBN : 9780821829691

Get Book

Braid and Knot Theory in Dimension Four by Seiichi Kamada Pdf

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.

A Gentle Introduction To Knots, Links And Braids

Ruben Aldrovandi,Roldao Da Rocha Jr
A Gentle Introduction To Knots Links And Braids Book PDF

Author : Ruben Aldrovandi,Roldao Da Rocha Jr
Publisher : World Scientific
Page : 214 pages
File Size : 49,6 Mb
Release : 2021-10-14
Category : Science
ISBN : 9789811248504

Get Book

A Gentle Introduction To Knots, Links And Braids by Ruben Aldrovandi,Roldao Da Rocha Jr Pdf

The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.

Knots, Links, Braids and 3-Manifolds

Viktor Vasilʹevich Prasolov,Alekseĭ Bronislavovich Sosinskiĭ
Knots Links Braids and 3 Manifolds Book PDF

Author : Viktor Vasilʹevich Prasolov,Alekseĭ Bronislavovich Sosinskiĭ
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 50,6 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821808986

Get Book

Knots, Links, Braids and 3-Manifolds by Viktor Vasilʹevich Prasolov,Alekseĭ Bronislavovich Sosinskiĭ Pdf

This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.

Encyclopedia of Knot Theory

Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson
Encyclopedia of Knot Theory Book PDF

Author : Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson
Publisher : CRC Press
Page : 954 pages
File Size : 42,7 Mb
Release : 2021-02-10
Category : Education
ISBN : 9781000222388

Get Book

Encyclopedia of Knot Theory by Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson Pdf

"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory

Low Dimensional Topology

Hanna Nencka
Low Dimensional Topology Book PDF

Author : Hanna Nencka
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 42,7 Mb
Release : 1999
Category : Low-dimensional topology
ISBN : 9780821808849

Get Book

Low Dimensional Topology by Hanna Nencka Pdf

"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.

Surface-Knots in 4-Space

Seiichi Kamada
Surface Knots in 4 Space Book PDF

Author : Seiichi Kamada
Publisher : Springer
Page : 212 pages
File Size : 44,6 Mb
Release : 2017-03-28
Category : Mathematics
ISBN : 9789811040917

Get Book

Surface-Knots in 4-Space by Seiichi Kamada Pdf

This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.Knot theory is one of the most active research fields in modern mathematics. Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are related to braids and 3-manifolds. These notions are generalized into higher dimensions. Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surface-knot theory treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example, knot concordance and knot cobordism, which are also important objects in knot theory, are surfaces in the product space of the 3-sphere and the interval.Included in this book are basics of surface-knots and the related topics of classical knots, the motion picture method, surface diagrams, handle surgeries, ribbon surface-knots, spinning construction, knot concordance and 4-genus, quandles and their homology theory, and two-dimensional braids.

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 : 43,9 Mb
Release : 2016-09-21
Category : Knot theory
ISBN : 9781470422578

Get Book

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.

Knots, Low-Dimensional Topology and Applications

Colin C. Adams,Cameron McA. Gordon,Vaughan F.R. Jones,Louis H. Kauffman,Sofia Lambropoulou,Kenneth C. Millett,Jozef H. Przytycki,Renzo Ricca,Radmila Sazdanovic
Knots Low Dimensional Topology and Applications Book PDF

Author : Colin C. Adams,Cameron McA. Gordon,Vaughan F.R. Jones,Louis H. Kauffman,Sofia Lambropoulou,Kenneth C. Millett,Jozef H. Przytycki,Renzo Ricca,Radmila Sazdanovic
Publisher : Springer
Page : 476 pages
File Size : 53,9 Mb
Release : 2019-06-26
Category : Mathematics
ISBN : 9783030160319

Get Book

Knots, Low-Dimensional Topology and Applications by Colin C. Adams,Cameron McA. Gordon,Vaughan F.R. Jones,Louis H. Kauffman,Sofia Lambropoulou,Kenneth C. Millett,Jozef H. Przytycki,Renzo Ricca,Radmila Sazdanovic Pdf

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.

Surfaces in 4-Space

Scott Carter,Seiichi Kamada,Masahico Saito
Surfaces in 4 Space Book PDF

Author : Scott Carter,Seiichi Kamada,Masahico Saito
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 52,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662101629

Get Book

Surfaces in 4-Space by Scott Carter,Seiichi Kamada,Masahico Saito Pdf

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.

Braid Group, Knot Theory and Statistical Mechanics

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

Author : C N Yang,M L Ge
Publisher : World Scientific
Page : 336 pages
File Size : 47,8 Mb
Release : 1991-06-05
Category : Electronic
ISBN : 9789814507424

Get Book

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

Contents:Notes on Subfactors and Statistical Mechanics (V F R Jones)Polynomial Invariants in Knot Theory (L H Kauffman)Algebras of Loops on Surfaces, Algebras of Knots, and Quantization (V G Turaev)Quantum Groups (L Faddeev et al.)Introduction to the Yang-Baxter Equation (M Jimbo)Integrable Systems Related to Braid Groups and Yang-Baxter Equation (T Kohno)The Yang-Baxter Relation: A New Tool for Knot Theory (Y Akutsu et al.)Akutsu-Wadati Link Polynomials from Feynman-Kauffman Diagrams (M-L Ge et al.)Quantum Field Theory and the Jones Polynomial (E Witten) Readership: Mathematical physicists.

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 : 54,5 Mb
Release : 1994-02-24
Category : Science
ISBN : 9789814502788

Get Book

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

Handbook of Knot Theory

William Menasco,Morwen Thistlethwaite
Handbook of Knot Theory Book PDF

Author : William Menasco,Morwen Thistlethwaite
Publisher : Elsevier
Page : 502 pages
File Size : 51,5 Mb
Release : 2005-08-02
Category : Mathematics
ISBN : 0080459544

Get Book

Handbook of Knot Theory by William Menasco,Morwen Thistlethwaite Pdf

This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry. * Survey of mathematical knot theory * Articles by leading world authorities * Clear exposition, not over-technical * Accessible to readers with undergraduate background in mathematics

Braid Group, Knot Theory, and Statistical Mechanics II

Chen Ning Yang,Mo-Lin Ge
Braid Group Knot Theory and Statistical Mechanics II Book PDF

Author : Chen Ning Yang,Mo-Lin Ge
Publisher : World Scientific
Page : 496 pages
File Size : 44,8 Mb
Release : 1994
Category : Science
ISBN : 981021524X

Get Book

Braid Group, Knot Theory, and Statistical Mechanics II by Chen Ning Yang,Mo-Lin 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.

Intelligence of Low Dimensional Topology 2006

J. Scott Carter
Intelligence of Low Dimensional Topology 2006 Book PDF

Author : J. Scott Carter
Publisher : World Scientific
Page : 398 pages
File Size : 50,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812770967

Get Book

Intelligence of Low Dimensional Topology 2006 by J. Scott Carter Pdf

This volume gathers the contributions from the international conference Intelligence of Low Dimensional Topology 2006, which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.

Diagrammatic Algebra

J. Scott Carter,Seiichi Kamada
Diagrammatic Algebra Book PDF

Author : J. Scott Carter,Seiichi Kamada
Publisher : American Mathematical Society
Page : 365 pages
File Size : 54,5 Mb
Release : 2021-12-15
Category : Mathematics
ISBN : 9781470466718

Get Book

Diagrammatic Algebra by J. Scott Carter,Seiichi Kamada Pdf

This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum field theory and knot theory. The text is replete with figures, diagrams, and suggestive typography that allows the reader a glimpse into many higher dimensional processes. The penultimate chapter summarizes the previous material by demonstrating how to braid 3- and 4- dimensional manifolds into 5- and 6-dimensional spaces. The book is accessible to post-qualifier graduate students, and will also be of interest to algebraists, topologists and algebraic topologists who would like to incorporate diagrammatic techniques into their research.