"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

Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition 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 profes-sional reference and will serve equally well as a text for a course on knot theory.

There has not been a scientific revolution for about 100 years. One seems imminent, as QED has recently been violated at the Sigma-6 level. Kuhn, in 'The Structure of Scientific Revolutions', used Wittgenstein's famous duck-rabbit optical illusion to demonstrate how bias in interpretation causes scientists to see the same information in radically different manners, which is likely to have delayed the pending paradigm shift. Jean-Pierre Vigier, continually labeled l'hérétique de la physique and l'eternel resistant in French media, remains a pillar of modern mathematical physics. 'Heretical' works of Vigier related to extended electromagnetic theory incorporating photon mass and a longitudinal B(3) EM field, gravity, quantum theory, large-scale additional dimensions, the Dirac polarized vacuum and many more related issues are deemed by his followers to be essential to the evolution of physics. The phrase 'Lives On' was chosen in the title of this volume to claim ignored portions of his work are relevant to implementing the Paradigm Shift to an Einsteinian Unified Field Theory. Specifically, chapters about the Dirac Hypertube, Tight-Bound States and Spacetime programming provide required insights into crossing the dimensional barrier and 'proving' parts of M-Theoretic dimensionality. As happens periodically in the history of science, we live in a climate where coloring outside-the-box can have severe myopic consequences such as difficulties in passing PhD exams, challenges in grant approval or problems in receiving tenure. Since there is no conflict with Gauge Theory, once realized, many chapters in this important volume will aid in facilitating progress in physics beyond the Standard Model.

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.

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.

Issues in Mathematical Theory and Modeling / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Lie Theory. The editors have built Issues in Mathematical Theory and Modeling: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Lie Theory in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Mathematical Theory and Modeling: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Since 1961, the Georgia Topology Conference has been held every eight years to discuss the newest developments in topology. The goals of the conference are to disseminate new and important results and to encourage interaction among topologists who are in different stages of their careers. Invited speakers are encouraged to aim their talks to a broad audience, and several talks are organized to introduce graduate students to topics of current interest. Each conference results in high-quality surveys, new research, and lists of unsolved problems, some of which are then formally published. Continuing in this 40-year tradition, the AMS presents this volume of articles and problem lists from the 2001 conference. Topics covered include symplectic and contact topology, foliations and laminations, and invariants of manifolds and knots. Articles of particular interest include John Etnyre's, ``Introductory Lectures on Contact Geometry'', which is a beautiful expository paper that explains the background and setting for many of the other papers. This is an excellent introduction to the subject for graduate students in neighboring fields. Etnyre and Lenhard Ng's, ``Problems in Low-Dimensional Contact Topology'' and Danny Calegari's extensive paper,``Problems in Foliations and Laminations of 3-Manifolds'' are carefully selected problems in keeping with the tradition of the conference. They were compiled by Etnyre and Ng and by Calegari with the input of many who were present. This book provides material of current interest to graduate students and research mathematicians interested in the geometry and topology of manifolds.

Propelled by the success of the sequencing of the human and many related genomes, molecular and cellular biology has delivered significant scientific breakthroughs. Mathematics (broadly defined) continues to play a major role in this effort, helping to discover the secrets of life by working collaboratively with bench biologists, chemists and physicists. Because of its outstanding record of interdisciplinary research and training, the IMA was an ideal venue for the 2007-2008 IMA thematic year on Mathematics of Molecular and Cellular Biology. The kickoff event for this thematic year was a tutorial on Mathematics of Nucleic Acids, followed by the workshop Mathematics of Molecular and Cellular Biology, held September 15--21 at the IMA. This volume is dedicated to the memory of Nicholas R. Cozzarelli, a dynamic leader who fostered research and training at the interface between mathematics and molecular biology. It contains a personal remembrance of Nick Cozzarelli, plus 15 papers contributed by workshop speakers. The papers give an overview of state-of-the-art mathematical approaches to the understanding of DNA structure and function, and the interaction of DNA with proteins that mediate vital life processes.