Download or read book Braid Groups written by Christian Kassel and published by Springer Science & Business Media. This book was released on 2008-06-28 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices. Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.
Download or read book Introduction to Complex Reflection Groups and Their Braid Groups written by Michel Broué and published by Springer. This book was released on 2010-01-28 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers basic properties of complex reflection groups, such as characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, including the basic findings of Springer theory on eigenspaces.
Download or read book Application of Braid Groups in 2D Hall System Physics written by Janusz Jacak and published by World Scientific. This book was released on 2012 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present treatise progress in topological approach to Hall system physics is reported, including recent achievements in graphene. The new homotopy methods of cyclotron braid subgroups, originally introduced by the authors, turn out to be of particular convenience in order to grasp peculiarity of 2D charged systems upon magnetic field resulting in fractional Hall states. The identified cyclotron braids allow for natural recovery of Laughlin correlations from the first principles, without invoking any artificial constructions as composite fermions with flux tubes or vortices. Progress in understanding of the structure and role of composite fermions in Hall system is provided, which can also lead to some corrections of numerical results in energy minimization made within the traditional formulation of the composite fermion model. The crucial significance of carrier mobility, apart from interaction in creation of the fractional quantum Hall effect (FQHE), is described and supported by recent graphene experiments. Recent advancement in the FQHE field including topological insulators and optical lattices is reviewed and commented upon in terms of the braid group approach. The braid group methods are presented from a more general point of view including proposition of pure braid group application. Book jacket.
Download or read book Braids Links and Mapping Class Groups AM 82 Volume 82 written by Joan S. Birman and published by Princeton University Press. This book was released on 2016-03-02 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.
Download or read book A Study of Braids written by Kunio Murasugi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Chapter 6, we describe the concept of braid equivalence from the topological point of view. This will lead us to a new concept braid homotopy that is discussed fully in the next chapter. As just mentioned, in Chapter 7, we shall discuss the difference between braid equivalence and braid homotopy. Also in this chapter, we define a homotopy braid invariant that turns out to be the so-called Milnor number. Chapter 8 is a quick review of knot theory, including Alexander's theorem. While, Chapters 9 is devoted to Markov's theorem, which allows the application of this theory to other fields. This was one of the motivations Artin had in mind when he began studying braid theory. In Chapter 10, we discuss the primary applications of braid theory to knot theory, including the introduction of the most important invariants of knot theory, the Alexander polynomial and the Jones polynomial. In Chapter 11, motivated by Dirac's string problem, the ordinary braid group is generalized to the braid groups of various surfaces. We discuss these groups from an intuitive and diagrammatic point of view. In the last short chapter 12, we present without proof one theorem, due to Gorin and Lin [GoL] , that is a surprising application of braid theory to the theory of algebraic equations.
Download or read book Ordering Braids written by Patrick Dehornoy and published by American Mathematical Soc.. This book was released on 2008 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the discovery that Artin's braid groups enjoy a left-invariant linear ordering, several different approaches have been used to understand this phenomenon. This text provides an account of those approaches, involving varied objects & domains as combinatorial group theory, self-distributive algebra & finite combinatorics.
Download or read book The Collected Papers of Wei Liang Chow written by Shiing-Shen Chern and published by World Scientific. This book was released on 2002 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book contains the collected papers of Prof Wei-Liang Chow, an original and versatile mathematician of the 20th Century. Prof Chow''s name has become a household word in mathematics because of the Chow ring, Chow coordinates, and Chow''s theorem on analytic sets in projective spaces. The Chow ring has many advantages and is widely used in intersection theory of algebraic geometry. Chow coordinates have been a very versatile tool in many aspects of algebraic geometry. Chow''s theorem OCo that a compact analytic variety in a projective space is algebraic OCo is justly famous; it shows the close analogy between algebraic geometry and algebraic number theory.About Professor Wei-Liang ChowThe long and distinguished career of Prof Wei-Liang Chow (1911OCo95) as a mathematician began in China with professorships at the National Central University in Nanking (1936OCo37) and the National Tung-Chi University in Shanghai (1946OCo47), and ultimately led him to the United States, where he joined the mathematics faculty of Johns Hopkins University in Baltimore, Maryland, first as an associate professor from 1948 to 1950, then as a full professor from 1950 until his retirement in 1977.In addition to serving as chairman of the mathematics department at Johns Hopkins from 1955 to 1965, he was Editor-in-Chief of the American Journal of Mathematics from 1953 to 1977."
Download or read book Braid Group Knot Theory And Statistical Mechanics written by Mo-lin Ge and published by World Scientific. This book was released on 1991-06-05 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Braids Links and Mapping Class Groups written by Joan S. Birman and published by Princeton University Press. This book was released on 1974 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.
Download or read book The Lower Algebraic K Theory of Virtually Cyclic Subgroups of the Braid Groups of the Sphere and of ZB4 S2 written by John Guaschi and published by Springer. This book was released on 2018-11-03 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven strings is computed using a wide variety of tools. Many of the techniques extend to the general case, and the results reveal new K-theoretical phenomena with respect to the previous study of other families of groups. The second part of the manuscript focusses on the case of the 4-string braid group of the 2-sphere, which is shown to be hyperbolic in the sense of Gromov. This permits the computation of the infinite maximal virtually cyclic subgroups of this group and their conjugacy classes, and applying the fact that this group satisfies the Fibred Isomorphism Conjecture of Farrell and Jones, leads to an explicit calculation of its lower K-theory. Researchers and graduate students working in K-theory and surface braid groups will constitute the primary audience of the manuscript, particularly those interested in the Fibred Isomorphism Conjecture, and the computation of Nil groups and the lower algebraic K-groups of group rings. The manuscript will also provide a useful resource to researchers who wish to learn the techniques needed to calculate lower algebraic K-groups, and the bibliography brings together a large number of references in this respect.
Download or read book Braids written by A. Jon Berrick and published by World Scientific. This book was released on 2010 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an indispensable guide for anyone seeking to familarize themselves with research in braid groups, configuration spaces and their applications. Starting at the beginning, and assuming only basic topology and group theory, the volume's noted expositors take the reader through the fundamental theory and on to current research and applications in fields as varied as astrophysics, cryptography and robotics. As leading researchers themselves, the authors write enthusiastically about their topics, and include many striking illustrations. The chapters have their origins in tutorials given at a Summer School on Braids, at the National University of Singapore's Institute for Mathematical Sciences in June 2007, to an audience of more than thirty international graduate students.
Download or read book Coding and Cryptography written by Øyvind Ytrehus and published by Springer Science & Business Media. This book was released on 2006-07-06 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the International Workshop on Coding and Cryptography, WCC 2005, held in Bergen, Norway, in March 2005. The 33 revised full papers were carefully reviewed and selected during two rounds of review. The papers address all aspects of coding theory, cryptography and related areas, theoretical or applied.
Download or read book The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups written by Daciberg Lima Goncalves and published by Springer Science & Business Media. This book was released on 2013-09-08 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This manuscript is devoted to classifying the isomorphism classes of the virtually cyclic subgroups of the braid groups of the 2-sphere. As well as enabling us to understand better the global structure of these groups, it marks an important step in the computation of the K-theory of their group rings. The classification itself is somewhat intricate, due to the rich structure of the finite subgroups of these braid groups, and is achieved by an in-depth analysis of their group-theoretical and topological properties, such as their centralisers, normalisers and cohomological periodicity. Another important aspect of our work is the close relationship of the braid groups with mapping class groups. This manuscript will serve as a reference for the study of braid groups of low-genus surfaces, and isaddressed to graduate students and researchers in low-dimensional, geometric and algebraic topology and in algebra.
Download or read book Homological Representations of Braid Groups written by Stephen John Bigelow and published by . This book was released on 2000 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Group Theory Statistics and Cryptography written by Alexei G. Myasnikov and published by American Mathematical Soc.. This book was released on 2004 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of contributions by speakers at the AMS Special Session on Combinatorial and Statistical Group Theory held at New York University. Readers will find a variety of contributions, including survey papers on applications of group theory in cryptography, research papers on various aspects of statistical group theory, and papers on more traditional combinatorial group theory. The book is suitable for graduate students and research mathematicians interested in group theory and its applications to cryptography.
Download or read book Configuration Spaces and Braid Groups of Graphs written by Aaron David Abrams and published by . This book was released on 2000 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Entanglement and Decoherence written by Andreas Buchleitner and published by Springer Science & Business Media. This book was released on 2008-11-25 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entanglement and (de-)coherence arguably define the central issues of concern in present day quantum information theory. Entanglement being a consequence of the quantum mechanical superposition principle for composite systems, a better understanding of the environment-induced destruction of coherent superposition states is required to devise novel strategies for harvesting quantum interference phenomena. The present book collects a series of advanced lectures on the theoretical foundations of this active research field, from mathematical aspects underlying quantum topology to mesoscopic transport theory. All lectures start out from an elementary level and proceed along a steep learning curve. This makes the material particularly suitable for student seminars on the more fundamental theoretical aspects of quantum information, and equally useful as supplementary reading for advanced lectures on this topic.
