Knot Theory And Manifolds
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Author |
: Lee Paul Neuwirth |
Publisher |
: Princeton University Press |
Total Pages |
: 346 |
Release |
: 2016-03-02 |
ISBN-10 |
: 9781400881512 |
ISBN-13 |
: 140088151X |
Rating |
: 4/5 (12 Downloads) |
Synopsis Knots, Groups and 3-Manifolds (AM-84), Volume 84 by : Lee Paul Neuwirth
There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers are dedicated to the memory of Ralph H. Fox, one of the world's leading topologists, by colleagues, former students, and friends. In knot theory, papers have been contributed by Goldsmith, Levine, Lomonaco, Perko, Trotter, and Whitten. Of these several are devoted to the study of branched covering spaces over knots and links, while others utilize the braid groups of Artin. Cossey and Smythe, Stallings, and Strasser address themselves to group theory. In his contribution Stallings describes the calculation of the groups In/In+1 where I is the augmentation ideal in a group ring RG. As a consequence, one has for each k an example of a k-generator l-relator group with no free homomorphs. In the third part, papers by Birman, Cappell, Milnor, Montesinos, Papakyriakopoulos, and Shalen comprise the treatment of 3-manifolds. Milnor gives, besides important new results, an exposition of certain aspects of our current knowledge regarding the 3- dimensional Brieskorn manifolds.
Author |
: Viktor Vasilʹevich Prasolov |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 250 |
Release |
: 1997 |
ISBN-10 |
: 9780821808986 |
ISBN-13 |
: 0821808982 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Knots, Links, Braids and 3-Manifolds by : Viktor Vasilʹevich Prasolov
This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.
Author |
: Dale Rolfsen |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 458 |
Release |
: 2003 |
ISBN-10 |
: 9780821834367 |
ISBN-13 |
: 0821834363 |
Rating |
: 4/5 (67 Downloads) |
Synopsis Knots and Links by : Dale Rolfsen
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 |
: Dale Rolfsen |
Publisher |
: Springer |
Total Pages |
: 168 |
Release |
: 2006-11-14 |
ISBN-10 |
: 9783540396161 |
ISBN-13 |
: 3540396160 |
Rating |
: 4/5 (61 Downloads) |
Synopsis Knot Theory and Manifolds by : Dale Rolfsen
Author |
: W.B.Raymond Lickorish |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 213 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461206910 |
ISBN-13 |
: 146120691X |
Rating |
: 4/5 (10 Downloads) |
Synopsis An Introduction to Knot Theory by : W.B.Raymond Lickorish
A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant results are achieved and each chapter ends with exercises and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area.
Author |
: Dale Rolfsen |
Publisher |
: |
Total Pages |
: 170 |
Release |
: 2014-09-01 |
ISBN-10 |
: 3662184745 |
ISBN-13 |
: 9783662184745 |
Rating |
: 4/5 (45 Downloads) |
Synopsis Knot Theory and Manifolds by : Dale Rolfsen
Author |
: Jessica S. Purcell |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 369 |
Release |
: 2020-10-06 |
ISBN-10 |
: 9781470454999 |
ISBN-13 |
: 1470454998 |
Rating |
: 4/5 (99 Downloads) |
Synopsis Hyperbolic Knot Theory by : Jessica S. Purcell
This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of Mostow and Prasad with Gordon and Luecke, it was known that a hyperbolic structure on a knot complement in the 3-sphere gives a complete knot invariant. However, it remains a difficult problem to relate the hyperbolic geometry of a knot to other invariants arising from knot theory. In particular, it is difficult to determine hyperbolic geometric information from a knot diagram, which is classically used to describe a knot. This textbook provides background on these problems, and tools to determine hyperbolic information on knots. It also includes results and state-of-the art techniques on hyperbolic geometry and knot theory to date. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises. The level is appropriate for graduate students with a basic background in algebraic topology, particularly fundamental groups and covering spaces. Some experience with some differential topology and Riemannian geometry will also be helpful.
Author |
: Colin Conrad Adams |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 330 |
Release |
: 2004 |
ISBN-10 |
: 9780821836781 |
ISBN-13 |
: 0821836781 |
Rating |
: 4/5 (81 Downloads) |
Synopsis The Knot Book by : Colin Conrad Adams
Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Author |
: Andrew Ranicki |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 669 |
Release |
: 2013-04-17 |
ISBN-10 |
: 9783662120118 |
ISBN-13 |
: 3662120119 |
Rating |
: 4/5 (18 Downloads) |
Synopsis High-dimensional Knot Theory by : Andrew Ranicki
Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory.
Author |
: Masanori Morishita |
Publisher |
: Springer Nature |
Total Pages |
: 268 |
Release |
: |
ISBN-10 |
: 9789819992553 |
ISBN-13 |
: 9819992559 |
Rating |
: 4/5 (53 Downloads) |
Synopsis Knots and Primes by : Masanori Morishita