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Author: Kunio Murasugi
Publisher: American Mathematical Soc.
ISBN: 9780821862315
Category : Mathematics
Languages : en
Pages : 120
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Book Description
* Presents a remarkable application of graph theory to knot theory
Author: Kunio Murasugi
Publisher: American Mathematical Soc.
ISBN: 9780821862315
Category : Mathematics
Languages : en
Pages : 120
Get Book Here
Book Description
* Presents a remarkable application of graph theory to knot theory
Author: Kunio Murasugi
Publisher: Springer Science & Business Media
ISBN: 0817647198
Category : Mathematics
Languages : en
Pages : 348
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Book Description
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.
Author: Akio Kawauchi
Publisher: Birkhäuser
ISBN: 3034892276
Category : Mathematics
Languages : en
Pages : 431
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Book Description
Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.
Author: Krishnendu Gongopadhyay
Publisher: American Mathematical Soc.
ISBN: 1470422573
Category : Mathematics
Languages : en
Pages : 376
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Book Description
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.
Author: Kunio Murasugi
Publisher: Oxford University Press, USA
ISBN: 9781470400859
Category : MATHEMATICS
Languages : en
Pages : 118
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Book Description
This book presents a remarkable application of graph theory to knot theory. In knot theory, there are a number of easily defined geometric invariants that are extremely difficult to compute; the braid index of a knot or link is one example. The authors evaluate the braid index for many knots and links using the generalized Jones polynomial and the index of a graph, a new invariant introduced here. This invariant, which is determined algorithmically, is likely to be of particular interest to computer scientists.
Author: Colin Conrad Adams
Publisher: American Mathematical Soc.
ISBN: 0821836781
Category : Mathematics
Languages : en
Pages : 330
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Book Description
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.
Author: Neil Robertson
Publisher: American Mathematical Soc.
ISBN: 0821851608
Category : Mathematics
Languages : en
Pages : 706
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Book Description
This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors, held at the University of Washington in Seattle in the summer of 1991. Among the topics covered are: algorithms on tree-structured graphs, well-quasi-ordering, logic, infinite graphs, disjoint path problems, surface embeddings, knot theory, graph polynomials, matroid theory, and combinatorial optimization.
Author: M.E. Bozhüyük
Publisher: Springer Science & Business Media
ISBN: 9401116954
Category : Mathematics
Languages : en
Pages : 355
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Book Description
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.
Author: American Mathematical Society. Short Course
Publisher: American Mathematical Soc.
ISBN: 0821844660
Category : Mathematics
Languages : en
Pages : 203
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Book Description
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.
Author: Dale Rolfsen
Publisher: American Mathematical Soc.
ISBN: 0821834363
Category : Mathematics
Languages : en
Pages : 458
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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.""
