Download or read book The Knot Book written by Colin Conrad Adams and published by American Mathematical Soc.. This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Functorial Knot Theory Categories Of Tangles Coherence Categorical Deformations And Topological Invariants written by David N Yetter and published by World Scientific. This book was released on 2001-04-16 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory.This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations.
Download or read book The Outdoor Knots Book written by Clyde Soles and published by The Mountaineers Books. This book was released on 2004-03-16 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: CLICK HERE TO DOWNLOAD A KNOT SAMPLER FROM THE CHAPTER ON "KNOTS FOR HIKING & CAMPING" (Provide us with a little information and we'll send your download directly to your inbox) * Guidelines for selecting the best rope and the best knot for the activity at hand * Knot-tying directions clearly illustrated with photos * New entry in the Mountaineers Outdoor Basics series It's fair to say that climber Clyde Soles is obsessed with ropes and knots and their absolute performance-since he regularly entrusts his life to ropes on sheer rock faces. His unique book explains how to select and use ropes, cordage, and webbing for the outdoors. Invaluable information is provided on rope handling techniques (how to avoid dreaded tangles) and the best methods for rope care and maintenance. Step-by-step directions for tying over 40 knots are clearly illustrated with photographs. Other useful features include a glossary and a knot comparison chart by activity. Chapters include Knots Basics (from Tripod Lashing to the Figure 8 Loop), Knots for Hikers and Climbers (from the Prusik knot to the Autoblock), Knots for Canoeists and Kayakers (from the Buntline hitch to the Bowline on a bight), and more. This is the definitive text on ropes and knots for anyone who plays in the outdoors!
Download or read book Introduction to Vassiliev Knot Invariants written by S. Chmutov and published by Cambridge University Press. This book was released on 2012-05-24 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed exposition of the theory with an emphasis on its combinatorial aspects.
Download or read book Complete Book of Fishing Knots Leaders and Lines written by Lindsey Philpott and published by Simon and Schuster. This book was released on 2015-05-05 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master every fishing knot you’ll ever need. When you’re fishing, there’s nothing more frustrating than letting a poorly tied knot cost you the catch of the day. Knot expert Lindsey Philpott has written a guide to save anglers everywhere that anguish. The Complete Book of Fishing Knots, Leaders, and Lines contains directions for fifty kinds of knots, ranging from easier knots for beginners to specialized knots for more experienced fishermen. Each knot is explained with step-by-step instructions and color photographs, all done using a thick monofilament to make them as easy to see as possible. Here are just a few of the various types of knots you’ll learn: Arbor Australian braid Palomar Japanese fisherman Bimini twist Paragum And many more! Also included is a glossary of terms to ensure that every part of the knot-tying process is easy to learn. The Complete Book of Fishing Knots, Leaders, and Lines offers clear instructions for tying winning leaders, tips for selecting lines, and up-to-date information from the field that will bring you the quickest, slickest, and best catch ever. Whether you’re trolling for huge marlin on the open seas or fishing for blue gill in your favorite fishing hole, this book is a must-have for fishermen of all abilities. Skyhorse Publishing is proud to publish a broad range of books for fishermen. Our books for anglers include titles that focus on fly fishing, bait fishing, fly-casting, spin casting, deep sea fishing, and surf fishing. Our books offer both practical advice on tackle, techniques, knots, and more, as well as lyrical prose on fishing for bass, trout, salmon, crappie, baitfish, catfish, and more. While not every title we publish becomes a New York Times bestseller or a national bestseller, we are committed to publishing books on subjects that are sometimes overlooked by other publishers and to authors whose work might not otherwise find a home.
Download or read book Introductory Lectures on Knot Theory written by Louis H. Kauffman and published by World Scientific. This book was released on 2012 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.
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.
Download or read book Applications of Knot Theory written by American Mathematical Society. Short Course and published by American Mathematical Soc.. This book was released on 2009 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Louis Kauffman discusses applications of knot theory to physics, Nadrian Seeman discusses how topology is used in DNA nanotechnology, and Jonathan Simon discusses the statistical and energetic properties of knots and their relation to molecular biology."--BOOK JACKET.
Download or read book Knot Theory and Its Applications written by Krishnendu Gongopadhyay and published by American Mathematical Soc.. This book was released on 2016-09-21 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the ICTS program Knot Theory and Its Applications (KTH-2013), held from December 10–20, 2013, at IISER Mohali, India. The meeting focused on the broad area of knot theory and its interaction with other disciplines of theoretical science. The program was divided into two parts. The first part was a week-long advanced school which consisted of minicourses. The second part was a discussion meeting that was meant to connect the school to the modern research areas. This volume consists of lecture notes on the topics of the advanced school, as well as surveys and research papers on current topics that connect the lecture notes with cutting-edge research in the broad area of knot theory.
Download or read book Physical and Numerical Models in Knot Theory written by Jorge Alberto Calvo and published by World Scientific. This book was released on 2005 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year.This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory.
Download or read book Linknot Knot Theory By Computer written by Slavik Vlado Jablan and published by World Scientific. This book was released on 2007-11-16 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: LinKnot — Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics.The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves.Hands-on computations using Mathematica or the webMathematica package LinKnot and beautiful illustrations facilitate better learning and understanding. LinKnot is also a powerful research tool for experimental mathematics implementation of Caudron's ideas. The use of Conway notation enables experimenting with large families of knots and links.Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata.
Download or read book An Interactive Introduction to Knot Theory written by Inga Johnson and published by Courier Dover Publications. This book was released on 2017-01-18 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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
Download or read book Physical Knots Knotting Linking and Folding Geometric Objects in mathbb R 3 written by Jorge Alberto Calvo and published by American Mathematical Soc.. This book was released on 2002 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The properties of knotted and linked configurations in space have long been of interest to physicists and mathematicians. More recently and more widely, they have become important to biologists, chemists, computer scientists, and engineers. The depth and breadth of their applications are widely appreciated. Nevertheless, fundamental and challenging questions remain to be answered. Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volumediscusses critical questions and introduces new ideas that will stimulate multi-disciplinary applications. Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others deal with applications of mathematics to theoretical computer science, engineering,physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti. This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.
Download or read book Encyclopedia of Knot Theory written by Colin Adams and published by CRC Press. This book was released on 2021-02-10 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Download or read book Topics in Knot Theory written by M.E. Bozhüyük and published by Springer Science & Business Media. This book was released on 1993-08-31 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Thief Knot written by Kate Milford and published by Clarion Books. This book was released on 2020 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: When Marzana's parents are recruited to solve an odd crime, she assembles her own team, including a ghost, to investigate the kidnapping.
