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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.

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29 pages on 20# paper in 60# covers, binder-ready ... Read more

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Knot theory. History of knot theory, Reidemeister move, Knotinvariant, Knot polynomial, Connected sum, Conway notation(knot theory), Contact geometry, Knots and graphs, List ofknot theory topics, Quantum topology, Knot (mathematics),William Thurston, Hyperbolic link, Chinese knotting,Unknotting problem ... Read more

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The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text.The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands. ... Read more

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This book is an introduction to classical knot theory. Topics covered include: different constructions of knots, knot diagrams, knot groups, fibred knots, characterisation of torus knots, prime decomposition of knots, cyclic coverings and Alexander polynomials and modules together with the free differential calculus, braids, branched coverings and knots, Montesinos links, representations of knot groups, surgery of 3-manifolds and knots.

Knot theory has expanded enormously since the first edition of this book published in 1985. A special feature of this second completely revised and extended edition is the introduction to two new constructions of knot invariants, namely the Jones and homfly polynomials and the Vassiliev invariants.

The book contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory.

Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known. The text is accessible to advanced undergraduate and graduate students in mathematics. ... Read more

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This digital document is an article from Science News, published by Thomson Gale on December 22, 2007. The length of the article is 1985 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Tied up in knots: anything that can tangle up, will, including DNA.
Author: Davide Castelvecchi
Publication: Science News (Magazine/Journal)
Date: December 22, 2007
Publisher: Thomson Gale
Volume: 172Issue: 25-26Page: 398(2)

Distributed by Thomson Gale ... Read more

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This book begins with the basic principles of circuits, derives their analytic properties in both the time and frequency domains, and states and proves the two important theorems. It then develops an algorithmic method to design common and uncommon types of circuits, such as prototype filters, lumped delay lines, constant phase difference circuits, and delay equalizers. The material also discusses the relation between gain and phase, linear and minimum phase functions, group delay, sensitivity functions, scattering matrix, synthesis of transfer functions, approximation of filter functions, all-pass circuits, and circuit design by optimization.

This book fills a need for a modern text on the mathematical foundations of passive circuits in general and passive filter design in particular. The mathematical foundations are what classical circuit theory, which is the subject of this book, is all about. It is old, but it has survived the test of time and it is still relevant today because it is basic.

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Who killed Tether Marlingspike?A knot is found brutally untied in her apartment. The police have no motive and no suspects. Until Tyler Trefoil, a recluse Bowline knot and dabbler in the 'forbidden maths' of the Topology, ties together the clues to arrive at the shocking truth. Based on Poe's Murder at the Rue Morgue, A Frayed Knot introduces Tyler Trefoil as the reclusive Bowline, Tether Marlingspike as the mohair yarn Clove Hitch victim, and Threddy Tassel as the whistle lanyard in search of redemption. ... Read more

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A Frayed Knot - Video Trailer
Watch Video Here: http://www.amazon.com/review/R32NICUU39UN8J Please enjoy this video trailer for 'A Frayed Knot'. ... Read more

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This volume consists of ten lectures given at an internationalworkshop/conference on knot theory held in July 1996 at WasedaUniversity Conference Center. It was organised by the InternationalResearch Institute of Mathematical Society of Japan. The workshop wasattended by nearly 170 mathematicians from Japan and 14 othercountries, most of whom were specialists in knot theory. The lecturescan serve as an introduction to the field for advanced undergraduates,graduates and also researchers working in areas such as theoreticalphysics. ... Read more

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This book contains new numerical isotopy invariants for knotsin the product of a surface (not necessarily orientable) with a lineand for links in 3-space. These invariants, called Gauss diagraminvariants, are defined in a combinatorial way using knot diagrams.The natural notion of global knots is introduced. Global knotsgeneralize closed braids. If the surface is not the disc or the spherethen there are Gauss diagram invariants which distinguish knots thatcannot be distinguished by quantum invariants. There are specificGauss diagram invariants of finite type for global knots. Theseinvariants, called T-invariants, separate global knots of some classesand it is conjectured that they separate all global knots.T-invariants cannot be obtained from the (generalized) Kontsevichintegral. Audience: The book is designed for research workers inlow-dimensional topology. ... Read more

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This highly readable text details the interaction between the mathematical theory of knots and the theories of surfaces and group presentations. It expertly introduces several topics critical to the development of pure mathematics while providing an account of math "in action" in an unusual context. Beginning with a simple diagrammatic approach to the study of knots that reflects the artistic and geometric appeal of interlaced forms, Knots and Surfaces takes the reader through recent research advances. Topics include topological spaces, surfaces, the fundamental group, graphs, free groups, and group presentations. The authors skillfully combine these topics to form a coherent and highly developed theory to explore and explain the accessible and intuitive problems of knots and surfaces to students and researchers in mathematics. ... Read more

Customer Reviews (1)

Unique approach; vibrant and captivating
This unique and vibrant book is an introductory book on knot theory that somehow sneaks in a lot more rigorous mathematics than you would expect.Without seeming overly difficult, it somehow manages to include a concise introduction to the basics of knot theory, basic topology, and even a little bit of graph theory, algebraic topology and the necessary algebra.

While assuming little background, this book covers an extraordinarily diverse range of material, and ties it all together.The book is written so that a third-year undergraduate could understand it, but it's interesting enough that a graduate student will still find it fascinating.

What I love most about this book is the choice and ordering of topics--the authors dive right into the material, going to some depth in exploring polynomial invariants before they even touch any "abstract nonsense" so to speak; the machinery is developed throughout the book, as it is needed, and as a result seems natural and fully motivated.

I think this book is excellent for self-study; it would also make a great textbook for a course, although to some extent the material in the course would be dictated by what the book covers.I also think that someone teaching a topology or graph theorycourses should keep this book in mind and recommend it to any students inquiring about connections to knot theory. ... Read more

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Appendicies A to I that are referenced by Volumes I and II in the theory of quantum torus knots (QTK). A detailed mathematical derivation of space curves is provided that links the diverse fields of superfluids, quantum mechanics, and hydrodynamics. ... Read more