Knots Low Dimensional Topology And Applications

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Knots, Low-Dimensional Topology and Applications

Author : Colin C. Adams
Publisher : Springer
ISBN 13 : 3030160319
Total Pages : 476 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Knots, Low-Dimensional Topology and Applications by : Colin C. Adams

Download or read book Knots, Low-Dimensional Topology and Applications written by Colin C. Adams and published by Springer. This book was released on 2019-06-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.

Knots, Links, Braids And 3-Manifolds

Author : Viktor Vasilʹevich Prasolov
Publisher :
ISBN 13 : 9781470445690
Total Pages : 250 pages
Book Rating : 4.4/5 (456 download)

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Book Synopsis Knots, Links, Braids And 3-Manifolds by : Viktor Vasilʹevich Prasolov

Download or read book Knots, Links, Braids And 3-Manifolds written by Viktor Vasilʹevich Prasolov and published by . This book was released on 1996 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Encyclopedia of Knot Theory

Author : Colin Adams
Publisher : Chapman & Hall/CRC
ISBN 13 : 9781138298217
Total Pages : 941 pages
Book Rating : 4.2/5 (982 download)

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Book Synopsis Encyclopedia of Knot Theory by : Colin Adams

Download or read book Encyclopedia of Knot Theory written by Colin Adams and published by Chapman & Hall/CRC. This book was released on 2021 with total page 941 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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 which is useful and accessible to undergraduates, post-graduates, 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 to by top researchers in the field of Knot Theory"--

New Ideas In Low Dimensional Topology

Author : Vassily Olegovich Manturov
Publisher : World Scientific
ISBN 13 : 9814630632
Total Pages : 540 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis New Ideas In Low Dimensional Topology by : Vassily Olegovich Manturov

Download or read book New Ideas In Low Dimensional Topology written by Vassily Olegovich Manturov and published by World Scientific. This book was released on 2015-01-27 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.

Low-Dimensional Topology

Author : R. Brown
Publisher : Cambridge University Press
ISBN 13 : 9780521281461
Total Pages : 260 pages
Book Rating : 4.2/5 (814 download)

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Book Synopsis Low-Dimensional Topology by : R. Brown

Download or read book Low-Dimensional Topology written by R. Brown and published by Cambridge University Press. This book was released on 1982-05-20 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of the proceedings of a conference held at the University College of North Wales (Bangor) in July of 1979. It assembles research papers which reflect diverse currents in low-dimensional topology. The topology of 3-manifolds, hyperbolic geometry and knot theory emerge as major themes. The inclusion of surveys of work in these areas should make the book very useful to students as well as researchers.

Low Dimensional Topology

Author : Samuel J. Lomonaco
Publisher : American Mathematical Soc.
ISBN 13 : 9780821853788
Total Pages : 360 pages
Book Rating : 4.8/5 (537 download)

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Book Synopsis Low Dimensional Topology by : Samuel J. Lomonaco

Download or read book Low Dimensional Topology written by Samuel J. Lomonaco and published by American Mathematical Soc.. This book was released on 1983-12-31 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume arose from a special session on Low Dimensional Topology organized and conducted by Dr. Lomonaco at the American Mathematical Society meeting held in San Francisco, California, January 7-11, 1981.

The Mathematics of Knots

Author : Markus Banagl
Publisher : Springer Science & Business Media
ISBN 13 : 3642156371
Total Pages : 363 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis The Mathematics of Knots by : Markus Banagl

Download or read book The Mathematics of Knots written by Markus Banagl and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quandles and Topological Pairs

Author : Takefumi Nosaka
Publisher : Springer
ISBN 13 : 9811067937
Total Pages : 136 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Quandles and Topological Pairs by : Takefumi Nosaka

Download or read book Quandles and Topological Pairs written by Takefumi Nosaka and published by Springer. This book was released on 2017-11-20 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics. The book is written from topological aspects, but it illustrates how esteemed quandle theory is in mathematics, and it constitutes a crash course for studying quandles.More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for the study of low-dimensional topology (e.g., knot theory) and relative objects with symmetry. The direction of research is summarized as “We shall thoroughly (re)interpret the previous studies of relative symmetry in terms of the quandle”. The perspectives contained herein can be summarized by the following topics. The first is on relative objects G/H, where G and H are groups, e.g., polyhedrons, reflection, and symmetric spaces. Next, central extensions of groups are discussed, e.g., spin structures, K2 groups, and some geometric anomalies. The third topic is a method to study relative information on a 3-dimensional manifold with a boundary, e.g., knot theory, relative cup products, and relative group cohomology.For applications in topology, it is shown that from the perspective that some existing results in topology can be recovered from some quandles, a method is provided to diagrammatically compute some “relative homology”. (Such classes since have been considered to be uncomputable and speculative). Furthermore, the book provides a perspective that unifies some previous studies of quandles.The former part of the book explains motivations for studying quandles and discusses basic properties of quandles. The latter focuses on low-dimensional topology or knot theory. Finally, problems and possibilities for future developments of quandle theory are posed.

Knots and Applications

Author : Louis H. Kauffman
Publisher : World Scientific
ISBN 13 : 9789810220044
Total Pages : 502 pages
Book Rating : 4.2/5 (2 download)

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Book Synopsis Knots and Applications by : Louis H. Kauffman

Download or read book Knots and Applications written by Louis H. Kauffman and published by World Scientific. This book was released on 1995 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Thomson) on the 19th century theory of vortex atoms, reprints of modern papers on knotted flux in physics and in fluid dynamics and knotted wormholes in general relativity. It also includes papers on Witten's approach to knots via quantum field theory and applications of this approach to quantum gravity and the Ising model in three dimensions. Other papers discuss the topology of RNA folding in relation to invariants of graphs and Vassiliev invariants, the entanglement structures of polymers, the synthesis of molecular Mobius strips and knotted molecules. The book begins with an article on the applications of knot theory to the foundations of mathematics and ends with an article on topology and visual perception. This volume will be of immense interest to all workers interested in new possibilities in the uses of knots and knot theory.

Knots, Braids, and Mapping Class Groups--papers Dedicated to Joan S. Birman

Author :
Publisher :
ISBN 13 : 9781470438142
Total Pages : 176 pages
Book Rating : 4.4/5 (381 download)

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Book Synopsis Knots, Braids, and Mapping Class Groups--papers Dedicated to Joan S. Birman by :

Download or read book Knots, Braids, and Mapping Class Groups--papers Dedicated to Joan S. Birman written by and published by . This book was released on 2001 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a number of specialties in low-dimensional topology that can find in their "family tree" a common ancestry in the theory of surface mappings. These include knot theory as studied through the use of braid representations and 3-manifolds as studied through the use of Heegaard splittings. The study of the surface mapping class group (the modular group) is of course a rich subject in its own right, with relations to many different fields of mathematics and theoretical physics. But its most direct and remarkable manifestation is probably in the vast area of low-dimensional topology. Altho.

Floer Homology, Gauge Theory, and Low-Dimensional Topology

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
ISBN 13 : 9780821838457
Total Pages : 318 pages
Book Rating : 4.8/5 (384 download)

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Book Synopsis Floer Homology, Gauge Theory, and Low-Dimensional Topology by : Clay Mathematics Institute. Summer School

Download or read book Floer Homology, Gauge Theory, and Low-Dimensional Topology written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2006 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in theearly 1980s, and was revolutionized by the introduction of the Seiberg-Witten equations in the mid-1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's constructionof an infinite-dimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material tothat presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds. Information for our distributors: Titles in this seriesare copublished with the Clay Mathematics Institute (Cambridge, MA).

Knots and Links

Author : Dale Rolfsen
Publisher : American Mathematical Soc.
ISBN 13 : 0821834363
Total Pages : 458 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Knots and Links by : Dale Rolfsen

Download or read book Knots and Links written by Dale Rolfsen and published by American Mathematical Soc.. This book was released on 2003 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.""

Low-Dimensional Geometry

Author : Francis Bonahon
Publisher : American Mathematical Soc.
ISBN 13 : 082184816X
Total Pages : 403 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Low-Dimensional Geometry by : Francis Bonahon

Download or read book Low-Dimensional Geometry written by Francis Bonahon and published by American Mathematical Soc.. This book was released on 2009-07-14 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.

Grid Homology for Knots and Links

Author : Peter S. Ozsváth
Publisher : American Mathematical Soc.
ISBN 13 : 1470417375
Total Pages : 410 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Grid Homology for Knots and Links by : Peter S. Ozsváth

Download or read book Grid Homology for Knots and Links written by Peter S. Ozsváth and published by American Mathematical Soc.. This book was released on 2015-12-04 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.

Knots

Author : Alekseĭ Bronislavovich Sosinskiĭ
Publisher : Harvard University Press
ISBN 13 : 9780674009448
Total Pages : 158 pages
Book Rating : 4.0/5 (94 download)

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Book Synopsis Knots by : Alekseĭ Bronislavovich Sosinskiĭ

Download or read book Knots written by Alekseĭ Bronislavovich Sosinskiĭ and published by Harvard University Press. This book was released on 2002 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by a mathematician known for his own work on knot theory, is a clear, concise, and engaging introduction to this complicated subject, and a guide to the basic ideas and applications of knot theory. 63 illustrations.

Handbook of Knot Theory

Author : William Menasco
Publisher : Elsevier
ISBN 13 : 9780080459547
Total Pages : 502 pages
Book Rating : 4.4/5 (595 download)

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Book Synopsis Handbook of Knot Theory by : William Menasco

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

Knot Theory and Its Applications

Author : Kunio Murasugi
Publisher : Springer Science & Business Media
ISBN 13 : 0817647198
Total Pages : 348 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Knot Theory and Its Applications by : Kunio Murasugi

Download or read book Knot Theory and Its Applications written by Kunio Murasugi and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.