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| Author | : Lee Paul Neuwirth |
| Publisher | : Princeton University Press |
| Total Pages | : 119 |
| Release | : 2016-03-02 |
| Genre | : Mathematics |
| ISBN | : 1400882036 |
The description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56, will be forthcoming.
| Author | : Lee Paul Neuwirth |
| Publisher | : Princeton University Press |
| Total Pages | : 124 |
| Release | : 1965-03-21 |
| Genre | : Mathematics |
| ISBN | : 9780691079912 |
The description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56, will be forthcoming.
| Author | : Hirotaka Akiyoshi |
| Publisher | : Lecture Notes in Mathematics |
| Total Pages | : 308 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : |
Here is the first part of a work that provides a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. It offers an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.
| Author | : Vassily Olegovich Manturov |
| Publisher | : CRC Press |
| Total Pages | : 417 |
| Release | : 2004-02-24 |
| Genre | : Mathematics |
| ISBN | : 0203402847 |
Since discovery of the Jones polynomial, knot theory has enjoyed a virtual explosion of important results and now plays a significant role in modern mathematics. In a unique presentation with contents not found in any other monograph, Knot Theory describes, with full proofs, the main concepts and the latest investigations in the field. The book is divided into six thematic sections. The first part discusses "pre-Vassiliev" knot theory, from knot arithmetics through the Jones polynomial and the famous Kauffman-Murasugi theorem. The second part explores braid theory, including braids in different spaces and simple word recognition algorithms. A section devoted to the Vassiliev knot invariants follows, wherein the author proves that Vassiliev invariants are stronger than all polynomial invariants and introduces Bar-Natan's theory on Lie algebra respresentations and knots. The fourth part describes a new way, proposed by the author, to encode knots by d-diagrams. This method allows the encoding of topological objects by words in a finite alphabet. Part Five delves into virtual knot theory and virtualizations of knot and link invariants. This section includes the author's own important results regarding new invariants of virtual knots. The book concludes with an introduction to knots in 3-manifolds and Legendrian knots and links, including Chekanov's differential graded algebra (DGA) construction. Knot Theory 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 professional reference and will serve equally well as a text for a course on knot theory.
| Author | : Jonathan Hillman |
| Publisher | : CUP Archive |
| Total Pages | : 180 |
| Release | : 1989-03-30 |
| Genre | : Mathematics |
| ISBN | : 9780521378123 |
To attack certain problems in 4-dimensional knot theory the author draws on a variety of techniques, focusing on knots in S^T4, whose fundamental groups contain abelian normal subgroups. Their class contains the most geometrically appealing and best understood examples. Moreover, it is possible to apply work in algebraic methods to these problems. Work in four-dimensional topology is applied in later chapters to the problem of classifying 2-knots.
| Author | : Charles Livingston |
| Publisher | : Cambridge University Press |
| Total Pages | : 276 |
| Release | : 1993 |
| Genre | : Mathematics |
| ISBN | : 9780883850275 |
This book uses only linear algebra and basic group theory to study the properties of knots.
| Author | : Hirotaka Akiyoshi |
| Publisher | : Springer |
| Total Pages | : 293 |
| Release | : 2007-05-26 |
| Genre | : Mathematics |
| ISBN | : 3540718079 |
Here is the first part of a work that provides a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. It offers an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.
| Author | : Dale Rolfsen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 458 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 0821834363 |
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.""
| Author | : M.E. Bozhüyük |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 355 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401116954 |
Topics in Knot Theory is a state of the art volume which presents surveys of the field by the most famous knot theorists in the world. It also includes the most recent research work by graduate and postgraduate students. The new ideas presented cover racks, imitations, welded braids, wild braids, surgery, computer calculations and plottings, presentations of knot groups and representations of knot and link groups in permutation groups, the complex plane and/or groups of motions. For mathematicians, graduate students and scientists interested in knot theory.
| Author | : Seiichi Kamada |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 329 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821829696 |
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.
