Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Properties Of Closed 3 Braids And Braid Representations Of Links
Download Properties Of Closed 3 Braids And Braid Representations Of Links full books in PDF, epub, and Kindle. Read online Properties Of Closed 3 Braids And Braid Representations Of Links ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Properties of Closed 3-Braids and Braid Representations of Links by : Alexander Stoimenow
Download or read book Properties of Closed 3-Braids and Braid Representations of Links written by Alexander Stoimenow and published by Springer. This book was released on 2017-11-29 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies diverse aspects of braid representations via knots and links. Complete classification results are illustrated for several properties through Xu’s normal 3-braid form and the Hecke algebra representation theory of link polynomials developed by Jones. Topological link types are identified within closures of 3-braids which have a given Alexander or Jones polynomial. Further classifications of knots and links arising by the closure of 3-braids are given, and new results about 4-braids are part of the work. Written with knot theorists, topologists,and graduate students in mind, this book features the identification and analysis of effective techniques for diagrammatic examples with unexpected properties.
Book Synopsis Braids, Links, and Mapping Class Groups by : Joan S. Birman
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.
Book Synopsis Knots, Low-Dimensional Topology and Applications by : Colin C. Adams
Download or read book Knots, Low-Dimensional Topology and Applications written by Colin C. Adams and published by Springer. This book was released on 2019-06-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Braids, Links, and Mapping Class Groups. (AM-82), Volume 82 by : Joan S. Birman
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.
Book Synopsis On Closed 3-Braids by : Kunio Murasugi
Download or read book On Closed 3-Braids written by Kunio Murasugi and published by American Mathematical Soc.. This book was released on 1974-12-31 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relationships between the conjugate classes of 3-braids and the link types of their closure are investigated, and it is shown that the product link type of closed pure 3-braid is determined by its conjugate class.
Book Synopsis History and Science of Knots by : J C Turner
Download or read book History and Science of Knots written by J C Turner and published by World Scientific. This book was released on 1996-05-30 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together twenty essays on diverse topics in the history and science of knots. It is divided into five parts, which deal respectively with knots in prehistory and antiquity, non-European traditions, working knots, the developing science of knots, and decorative and other aspects of knots. Its authors include archaeologists who write on knots found in digs of ancient sites (one describes the knots used by the recently discovered Ice Man); practical knotters who have studied the history and uses of knots at sea, for fishing and for various life support activities; a historian of lace; a computer scientist writing on computer classification of doilies; and mathematicians who describe the history of knot theories from the eighteenth century to the present day. In view of the explosion of mathematical theories of knots in the past decade, with consequential new and important scientific applications, this book is timely in setting down a brief, fragmentary history of mankind's oldest and most useful technical and decorative device — the knot. Contents:Prehistory and Antiquity:Pleistocene KnottingWhy Knot? — Some Speculations on the First KnotsOn Knots and Swamps — Knots in European PrehistoryAncient Egyptian Rope and KnotsNon-European Traditions:The Peruvian QuipuThe Art of Chinese Knots Works: A Short HistoryInuit KnotsWorking Knots:Knots at SeaA History of Life Support KnotsTowards a Science of Knots?:Studies on the Behaviour of KnotsA History of Topological Knot Theory of KnotsTramblesCrochet Work — History and Computer ApplicationsDecorative Knots and Other Aspects:The History of MacraméA History of LaceHeraldic KnotsOn the True Love Knotand other papers Readership: Mathematicians, archeologists, social historians and general readers. keywords:Antiquit;Braiding;Climbing;Heraldry;History;Knots;Lace;Mariners;Prehistory;Quipus;Science;Theory;Topology;Knotting, Pleistocene;Egyptian;Inuit;Chinese;Mountaineering, Topological Knot Theory;Knot Theories;Quipo Knot Mathematics;Knot Strength Efficiency;Heraldic;True Love;Crochet;Computer Aided Design;Trambles “… it is a veritable compendium of information about every aspects of knots, from their links with quantum theory to attempts to measure their strength when tying climbing ropes together … the huge scope of this book makes it one I have turned to many times, for many different purposes.” New Scientists “I enjoyed browsing through all the chapters. They contain material that a mathematician would not normally come across in his work.” The Mathematical Intelligencer
Book Synopsis Diagram Genus, Generators, and Applications by : Alexander Stoimenow
Download or read book Diagram Genus, Generators, and Applications written by Alexander Stoimenow and published by CRC Press. This book was released on 2018-09-03 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: In knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns ("generators"). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems. The book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators using Hirasawa’s algorithm and extends this description to push the compilation of knot generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of the genus 4 classification, including the braid index, polynomial invariants, hyperbolic volume, and Vassiliev invariants. The final chapter presents further research related to generators, which helps readers see applications of generators in a broader context.
Book Synopsis Knot Theory by : Vassily Olegovich Manturov
Download or read book Knot Theory written by Vassily Olegovich Manturov and published by CRC Press. This book was released on 2018-04-17 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition is notable not only for its expert presentation of knot theory’s state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.
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.
Book Synopsis New Developments in the Theory of Knots by :
Download or read book New Developments in the Theory of Knots written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Braids and Coverings by : Vagn Lundsgaard Hansen
Download or read book Braids and Coverings written by Vagn Lundsgaard Hansen and published by Cambridge University Press. This book was released on 1989-12-07 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essays develop the elementary theory of Artin Braid groups geometrically and via homotopy theory, discuss the link between knot theory and the combinatorics of braid groups through Markou's Theorem and investigate polynomial covering maps.
Book Synopsis A Survey of Knot Theory by : Akio Kawauchi
Download or read book A Survey of Knot Theory written by Akio Kawauchi and published by Birkhäuser. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.
Book Synopsis Handbook of Knot Theory by : William Menasco
Download or read book Handbook of Knot Theory written by William Menasco and published by Elsevier. This book was released on 2005-08-02 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Cycles and Rays written by Gena Hahn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is the "archetypal" image that comes to mind when one thinks of an infinite graph? What with a finite graph - when it is thought of as opposed to an infinite one? What structural elements are typical for either - by their presence or absence - yet provide a common ground for both? In planning the workshop on "Cycles and Rays" it had been intended from the outset to bring infinite graphs to the fore as much as possible. There never had been a graph theoretical meeting in which infinite graphs were more than "also rans", let alone one in which they were a central theme. In part, this is a matter of fashion, inasmuch as they are perceived as not readily lending themselves to applications, in part it is a matter of psychology stemming from the insecurity that many graph theorists feel in the face of set theory - on which infinite graph theory relies to a considerable extent. The result is that by and large, infinite graph theorists know what is happening in finite graphs but not conversely. Lack of knowledge about infinite graph theory can also be found in authoritative l sources. For example, a recent edition (1987) of a major mathematical encyclopaedia proposes to ". . . restrict [itself] to finite graphs, since only they give a typical theory". If anything, the reverse is true, and needless to say, the graph theoretical world knows better. One may wonder, however, by how much.
Book Synopsis Number Theory and Symmetry by : Michel Planat
Download or read book Number Theory and Symmetry written by Michel Planat and published by MDPI. This book was released on 2021-01-20 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal’s triangle). The book should be of interest to all mathematicians, and physicists.
Book Synopsis Canadian Journal of Mathematics by :
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1989-04 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Knots and Links written by Dale Rolfsen and published by American Mathematical Soc.. This book was released on 2003 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book.""
