Formal Knot Theory PDF Download
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Author | : Louis H. Kauffman |
Publisher | : Courier Corporation |
Total Pages | : 274 |
Release | : 2006-01-01 |
Genre | : Mathematics |
ISBN | : 048645052X |
Download Formal Knot Theory Book in PDF, ePub and Kindle
This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author, Louis H. Kauffman, is a professor in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago. Kauffman draws upon his work as a topologist to illustrate the relationships between knot theory and statistical mechanics, quantum theory, and algebra, as well as the role of knot theory in combinatorics. Featured topics include state, trails, and the clock theorem; state polynomials and the duality conjecture; knots and links; axiomatic link calculations; spanning surfaces; the genus of alternative links; and ribbon knots and the Arf invariant. Key concepts are related in easy-to-remember terms, and numerous helpful diagrams appear throughout the text. The author has provided a new supplement, entitled "Remarks on Formal Knot Theory," as well as his article, "New Invariants in the Theory of Knots," first published in The American Mathematical Monthly, March 1988.
Author | : Louis H. Kauffman |
Publisher | : |
Total Pages | : 167 |
Release | : 1983 |
Genre | : Mathematics |
ISBN | : 9780691083360 |
Download Formal Knot Theory Book in PDF, ePub and Kindle
The Description for this book, Formal Knot Theory. (MN-30): , will be forthcoming.
Author | : Inga Johnson |
Publisher | : Courier Dover Publications |
Total Pages | : 192 |
Release | : 2017-01-04 |
Genre | : Mathematics |
ISBN | : 0486818748 |
Download An Interactive Introduction to Knot Theory Book in PDF, ePub and Kindle
This well-written and engaging volume, intended for undergraduates, introduces knot theory, an area of growing interest in contemporary mathematics. The hands-on approach features many exercises to be completed by readers. Prerequisites are only a basic familiarity with linear algebra and a willingness to explore the subject in a hands-on manner. The opening chapter offers activities that explore the world of knots and links — including games with knots — and invites the reader to generate their own questions in knot theory. Subsequent chapters guide the reader to discover the formal definition of a knot, families of knots and links, and various knot notations. Additional topics include combinatorial knot invariants, knot polynomials, unknotting operations, and virtual knots.
Author | : Colin Conrad Adams |
Publisher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821836781 |
Download The Knot Book Book in PDF, ePub and Kindle
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 | : Kunio Murasugi |
Publisher | : Springer Science & Business Media |
Total Pages | : 348 |
Release | : 2009-12-29 |
Genre | : Mathematics |
ISBN | : 0817647198 |
Download Knot Theory and Its Applications Book in PDF, ePub and Kindle
This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.
Author | : Louis H. Kauffman |
Publisher | : Princeton University Press |
Total Pages | : 500 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : 9780691084350 |
Download On Knots Book in PDF, ePub and Kindle
On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial. Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.
Author | : Colin Adams |
Publisher | : CRC Press |
Total Pages | : 954 |
Release | : 2021-02-10 |
Genre | : Education |
ISBN | : 1000222381 |
Download Encyclopedia of Knot Theory Book in PDF, ePub and Kindle
"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory
Author | : R. H. Crowell |
Publisher | : Springer Science & Business Media |
Total Pages | : 191 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461299357 |
Download Introduction to Knot Theory Book in PDF, ePub and Kindle
Knot theory is a kind of geometry, and one whose appeal is very direct because the objects studied are perceivable and tangible in everyday physical space. It is a meeting ground of such diverse branches of mathematics as group theory, matrix theory, number theory, algebraic geometry, and differential geometry, to name some of the more prominent ones. It had its origins in the mathematical theory of electricity and in primitive atomic physics, and there are hints today of new applications in certain branches of chemistryJ The outlines of the modern topological theory were worked out by Dehn, Alexander, Reidemeister, and Seifert almost thirty years ago. As a subfield of topology, knot theory forms the core of a wide range of problems dealing with the position of one manifold imbedded within another. This book, which is an elaboration of a series of lectures given by Fox at Haverford College while a Philips Visitor there in the spring of 1956, is an attempt to make the subject accessible to everyone. Primarily it is a text book for a course at the junior-senior level, but we believe that it can be used with profit also by graduate students. Because the algebra required is not the familiar commutative algebra, a disproportionate amount of the book is given over to necessary algebraic preliminaries.
Author | : Andrew Ranicki |
Publisher | : Springer Science & Business Media |
Total Pages | : 669 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662120119 |
Download High-dimensional Knot Theory Book in PDF, ePub and Kindle
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 | : Inga Johnson |
Publisher | : Courier Dover Publications |
Total Pages | : 193 |
Release | : 2017-01-18 |
Genre | : Mathematics |
ISBN | : 0486804631 |
Download An Interactive Introduction to Knot Theory Book in PDF, ePub and Kindle
This well-written and engaging volume, intended for undergraduates, introduces knot theory, an area of growing interest in contemporary mathematics. The hands-on approach features many exercises to be completed by readers. Prerequisites are only a basic familiarity with linear algebra and a willingness to explore the subject in a hands-on manner. The opening chapter offers activities that explore the world of knots and links — including games with knots — and invites the reader to generate their own questions in knot theory. Subsequent chapters guide the reader to discover the formal definition of a knot, families of knots and links, and various knot notations. Additional topics include combinatorial knot invariants, knot polynomials, unknotting operations, and virtual knots.