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On Closed 3 Braids
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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 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 New Developments in the Theory of Knots by : Toshitake Kohno
Download or read book New Developments in the Theory of Knots written by Toshitake Kohno and published by World Scientific. This book was released on 1990 with total page 924 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
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 Braid and Knot Theory in Dimension Four by : Seiichi Kamada
Download or read book Braid and Knot Theory in Dimension Four written by Seiichi Kamada and published by American Mathematical Soc.. This book was released on 2002 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Topological Fluid Mechanics by : Mitchell A. Berger
Download or read book Lectures on Topological Fluid Mechanics written by Mitchell A. Berger and published by Springer Science & Business Media. This book was released on 2009-05-05 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Book Synopsis Braid Foliations in Low-Dimensional Topology by : Douglas J. LaFountain
Download or read book Braid Foliations in Low-Dimensional Topology written by Douglas J. LaFountain and published by American Mathematical Soc.. This book was released on 2017-10-20 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Knots 90 written by Akio Kawauchi and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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.
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
Book Synopsis The Mathematical Theory of Knots and Braids by : S. Moran
Download or read book The Mathematical Theory of Knots and Braids written by S. Moran and published by Elsevier. This book was released on 2000-04-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of knots via the theory of braids, which attempts to be complete in a number of ways. Some knowledge of Topology is assumed. Necessary Group Theory and further necessary Topology are given in the book. The exposition is intended to enable an interested reader to learn the basics of the subject. Emphasis is placed on covering the theory in an algebraic way. The work includes quite a number of worked examples. The latter part of the book is devoted to previously unpublished material.
Book Synopsis Surveys in Contemporary Mathematics by : Nicholas Young
Download or read book Surveys in Contemporary Mathematics written by Nicholas Young and published by Cambridge University Press. This book was released on 2008 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.
Download or read book Braids written by Joan S. Birman and published by American Mathematical Soc.. This book was released on 1988 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: Artin introduced braid groups into mathematical literature in 1925. In the years since, and particularly in the last five to ten years, braid groups have played diverse and unexpected roles in widely different areas of mathematics, including knot theory, homotopy theory, singularity theory, and dynamical systems. Most recently, the area of operator algebras has brought striking new applications to knots and links. This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group, held at the University of California, Santa Cruz, in July 1986. This interdisciplinary conference brought together leading specialists in diverse areas of mathematics to discuss their discoveries and to exchange ideas and problems concerning this important and fundamental group. Because the proceedings present a mix of expository articles and new research, this volume will be of interest to graduate students and researchers who wish to learn more about braids, as well as more experienced workers in this area. The required background includes the basics of knot theory, group theory, and low-dimensional topology.
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 Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory by : Vassily Olegovich Manturov
Download or read book Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory written by Vassily Olegovich Manturov and published by World Scientific. This book was released on 2020-04-22 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups — Γnk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.
Book Synopsis Low Dimensional Topology by : Hanna Nencka
Download or read book Low Dimensional Topology written by Hanna Nencka and published by American Mathematical Soc.. This book was released on 1999 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Intelligence of Low Dimensional Topology 2006 by : J. Scott Carter
Download or read book Intelligence of Low Dimensional Topology 2006 written by J. Scott Carter and published by World Scientific. This book was released on 2007 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
