Topological Quandles and Invariants of Links PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Topological Quandles and Invariants of Links PDF full book. Access full book title Topological Quandles and Invariants of Links by Ryszard L. Rubinsztein. Download full books in PDF and EPUB format.
Author: Ryszard L. Rubinsztein
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
Get Book Here
Book Description
Author: Ryszard L. Rubinsztein
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
Get Book Here
Book Description
Author: Viktor Vasilʹevich Prasolov
Publisher: American Mathematical Soc.
ISBN: 0821808982
Category : Mathematics
Languages : en
Pages : 250
Get Book Here
Book Description
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. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.
Author: Takefumi Nosaka
Publisher: Springer
ISBN: 9811067937
Category : Mathematics
Languages : en
Pages : 138
Get Book Here
Book Description
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.
Author: Mohamed Elhamdadi
Publisher: American Mathematical Soc.
ISBN: 1470422131
Category : Mathematics
Languages : en
Pages : 257
Get Book Here
Book Description
From prehistory to the present, knots have been used for purposes both artistic and practical. The modern science of Knot Theory has ramifications for biochemistry and mathematical physics and is a rich source of research projects for undergraduate and graduate students and professionals alike. Quandles are essentially knots translated into algebra. This book provides an accessible introduction to quandle theory for readers with a background in linear algebra. Important concepts from topology and abstract algebra motivated by quandle theory are introduced along the way. With elementary self-contained treatments of topics such as group theory, cohomology, knotted surfaces and more, this book is perfect for a transition course, an upper-division mathematics elective, preparation for research in knot theory, and any reader interested in knots.
Author: A. B. Sossinsky
Publisher: American Mathematical Society
ISBN: 1470471515
Category : Mathematics
Languages : en
Pages : 149
Get Book Here
Book Description
This book is an elementary introduction to knot theory. Unlike many other books on knot theory, this book has practically no prerequisites; it requires only basic plane and spatial Euclidean geometry but no knowledge of topology or group theory. It contains the first elementary proof of the existence of the Alexander polynomial of a knot or a link based on the Conway axioms, particularly the Conway skein relation. The book also contains an elementary exposition of the Jones polynomial, HOMFLY polynomial and Vassiliev knot invariants constructed using the Kontsevich integral. Additionally, there is a lecture introducing the braid group and shows its connection with knots and links. Other important features of the book are the large number of original illustrations, numerous exercises and the absence of any references in the first eleven lectures. The last two lectures differ from the first eleven: they comprise a sketch of non-elementary topics and a brief history of the subject, including many references.
Author: Dale Rolfsen
Publisher: American Mathematical Soc.
ISBN: 0821834363
Category : Mathematics
Languages : en
Pages : 458
Get Book Here
Book Description
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.""
Author: Scott Carter
Publisher: Springer Science & Business Media
ISBN: 3662101629
Category : Mathematics
Languages : en
Pages : 220
Get Book Here
Book Description
Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory are presented. The last chapter comprises many recent results, and techniques for computation are presented. New tables of quandles with a few elements and the homology groups thereof are included. This book contains many new illustrations of knotted surface diagrams. The reader of the book will become intimately aware of the subtleties in going from the classical case of knotted circles in 3-space to this higher dimensional case. As a survey, the book is a guide book to the extensive literature on knotted surfaces and will become a useful reference for graduate students and researchers in mathematics and physics.
Author: J. Scott Carter
Publisher: World Scientific
ISBN: 9812705937
Category : Science
Languages : en
Pages : 398
Get Book Here
Book Description
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.
Author: David N. Yetter
Publisher: World Scientific
ISBN: 9810244436
Category : Mathematics
Languages : en
Pages : 238
Get Book Here
Book Description
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.
Author: Vassily Olegovich Manturov
Publisher: CRC Press
ISBN: 0203402847
Category : Mathematics
Languages : en
Pages : 417
Get Book Here
Book Description
Since discovery of the Jones polynomial, knot theory has enjoyed a virtual explosion of important results and now plays a significant role in modern mathematics. In a unique presentation with contents not found in any other monograph, Knot Theory describes, with full proofs, the main concepts and the latest investigations in the field. The book is divided into six thematic sections. The first part discusses "pre-Vassiliev" knot theory, from knot arithmetics through the Jones polynomial and the famous Kauffman-Murasugi theorem. The second part explores braid theory, including braids in different spaces and simple word recognition algorithms. A section devoted to the Vassiliev knot invariants follows, wherein the author proves that Vassiliev invariants are stronger than all polynomial invariants and introduces Bar-Natan's theory on Lie algebra respresentations and knots. The fourth part describes a new way, proposed by the author, to encode knots by d-diagrams. This method allows the encoding of topological objects by words in a finite alphabet. Part Five delves into virtual knot theory and virtualizations of knot and link invariants. This section includes the author's own important results regarding new invariants of virtual knots. The book concludes with an introduction to knots in 3-manifolds and Legendrian knots and links, including Chekanov's differential graded algebra (DGA) construction. Knot Theory 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 professional reference and will serve equally well as a text for a course on knot theory.
