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Author: Kunio Murasugi
Publisher: American Mathematical Soc.
Published: 1974-12-31
Total Pages: 122
ISBN-13: 0821818511
DOWNLOAD EBOOKThe 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.
Author: Alexander Stoimenow
Publisher: Springer
Published: 2017-11-29
Total Pages: 115
ISBN-13: 3319681494
DOWNLOAD EBOOKThis 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.
Author: Toshitake Kohno
Publisher: World Scientific
Published: 1990-08-31
Total Pages: 918
ISBN-13: 9814507016
DOWNLOAD EBOOKThis reprint volume focuses on recent developments in knot theory arising from mathematical physics, especially solvable lattice models, Yang-Baxter equation, quantum group and two dimensional conformal field theory. This volume is helpful to topologists and mathematical physicists because existing articles are scattered in journals of many different domains including Mathematics and Physics. This volume will give an excellent perspective on these new developments in Topology inspired by mathematical physics.
Author: Christian Kassel
Publisher: Springer Science & Business Media
Published: 2008-06-28
Total Pages: 349
ISBN-13: 0387685480
DOWNLOAD EBOOKIn 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.
Author: Seiichi Kamada
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 329
ISBN-13: 0821829696
DOWNLOAD EBOOKBraid 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.
Author: Mitchell A. Berger
Publisher: Springer Science & Business Media
Published: 2009-05-05
Total Pages: 240
ISBN-13: 3642008364
DOWNLOAD EBOOKThis volume contains a wide-ranging collection of valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics to DNA tangles and knotted DNAs in sedimentation.
Author: Akio Kawauchi
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 431
ISBN-13: 3034892276
DOWNLOAD EBOOKKnot 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.
Author: Douglas J. LaFountain
Publisher: American Mathematical Soc.
Published: 2017-10-20
Total Pages: 305
ISBN-13: 1470436604
DOWNLOAD EBOOKOffers a self-contained introduction to braid foliation techniques, which is a theory developed to study knots, links and surfaces in general 3-manifolds and more specifically in contact 3-manifolds. With style and content accessible to beginning students interested in geometric topology, each chapter centres around a key theorem or theorems.
Author: Joan S. Birman
Publisher: Princeton University Press
Published: 2016-03-02
Total Pages: 237
ISBN-13: 1400881420
DOWNLOAD EBOOKThe 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.
Author: Akio Kawauchi
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2014-07-24
Total Pages: 652
ISBN-13: 3110875918
DOWNLOAD EBOOKThe series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
