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.

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.

Intelligence of Low Dimensional Topology 2006

Author : J. Scott Carter
Publisher : World Scientific
ISBN 13 : 9812770968
Total Pages : 398 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Intelligence of Low Dimensional Topology 2006 by : J. Scott Carter

Download or read book Intelligence of Low Dimensional Topology 2006 written by J. Scott Carter and published by World Scientific. This book was released on 2007 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers the contributions from the international conference Intelligence of Low Dimensional Topology 2006, which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.

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"--

Knots, Links, Braids, and 3-manifolds

Author : V. V. Prasolov
Publisher : American Mathematical Soc.
ISBN 13 : 0821808982
Total Pages : 239 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Knots, Links, Braids, and 3-manifolds by : V. V. Prasolov

Download or read book Knots, Links, Braids, and 3-manifolds written by V. V. Prasolov and published by American Mathematical Soc.. This book was released on 1997 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. It emphasizes the geometric aspects of the theory and treats topics such as braids, homeomorphisms of surfaces, surgery of 3-manifolds (Kirby calculus), and branched coverings. This attractive geometric material, interesting in itself yet not previously gathered in book form, constitutes the basis of the last two chapters, where the Jones-Witten invariants are constructed via the rigorous skein algebra approach (mainly due to the Saint Petersburg school). Unlike several recent monographs, where all of these invariants are introduced by using the sophisticated abstract algebra of quantum groups and representation theory, the mathematical prerequisites are minimal in this book. Numerous figures and problems make it suitable as a course text and for self-study.

Low Dimensional Topology

Author : Tomasz Mrowka
Publisher : American Mathematical Soc.
ISBN 13 : 0821886967
Total Pages : 331 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Low Dimensional Topology by : Tomasz Mrowka

Download or read book Low Dimensional Topology written by Tomasz Mrowka and published by American Mathematical Soc.. This book was released on 2009-01-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-dimensional topology has long been a fertile area for the interaction of many different disciplines of mathematics, including differential geometry, hyperbolic geometry, combinatorics, representation theory, global analysis, classical mechanics, and theoretical physics. The Park City Mathematics Institute summer school in 2006 explored in depth the most exciting recent aspects of this interaction, aimed at a broad audience of both graduate students and researchers. The present volume is based on lectures presented at the summer school on low-dimensional topology. These notes give fresh, concise, and high-level introductions to these developments, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field of low-dimensional topology and to senior researchers wishing to keep up with current developments. The volume begins with notes based on a special lecture by John Milnor about the history of the topology of manifolds. It also contains notes from lectures by Cameron Gordon on the basics of three-manifold topology and surgery problems, Mikhail Khovanov on his homological invariants for knots, John Etnyre on contact geometry, Ron Fintushel and Ron Stern on constructions of exotic four-manifolds, David Gabai on the hyperbolic geometry and the ending lamination theorem, Zoltan Szabo on Heegaard Floer homology for knots and three manifolds, and John Morgan on Hamilton's and Perelman's work on Ricci flow and geometrization.

Low Dimensional Topology

Author : Samuel J. Lomonaco
Publisher : American Mathematical Soc.
ISBN 13 : 0821850164
Total Pages : 346 pages
Book Rating : 4.8/5 (218 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 with total page 346 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.

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.

Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory

Author : Vassily Olegovich Manturov
Publisher : World Scientific
ISBN 13 : 9811220131
Total Pages : 387 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory by : Vassily Olegovich Manturov

Download or read book Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory written by Vassily Olegovich Manturov and published by World Scientific. This book was released on 2020-04-22 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups — Γnk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.

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.

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.

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 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.

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, 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.