An Index of a Graph with Applications to Knot Theory
An Index of a Graph with Applications to Knot Theory

Author: Kunio Murasugi

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 118

ISBN-13: 0821825704

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There are three chapters to the memoir. The first defines and develops the notion of the index of a graph. The next chapter presents the general application of the graph index to knot theory. The last section is devoted to particular examples, such as determining the braid index of alternating pretzel links. A second result shows that for an alternating knot with Alexander polynomial having leading coefficient less than 4 in absolute value, the braid index is determined by polynomial invariants.

Knot Theory and Its Applications
Knot Theory and Its Applications

Author: Kunio Murasugi

Publisher: Springer Science & Business Media

Published: 2009-12-29

Total Pages: 348

ISBN-13: 0817647198

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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.

The Knot Book
The Knot Book

Author: Colin Conrad Adams

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 330

ISBN-13: 0821836781

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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.

Index of a Graph with Applications to Knot Theory
Index of a Graph with Applications to Knot Theory

Author: Kunio Murasugi

Publisher: Oxford University Press, USA

Published: 2014-08-31

Total Pages: 118

ISBN-13: 9781470400859

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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.

Knot Theory and Its Applications
Knot Theory and Its Applications

Author: Krishnendu Gongopadhyay

Publisher: American Mathematical Soc.

Published: 2016-09-21

Total Pages: 376

ISBN-13: 1470422573

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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.

A Survey of Knot Theory
A Survey of Knot Theory

Author: Akio Kawauchi

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 431

ISBN-13: 3034892276

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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.

Handbook of Knot Theory
Handbook of Knot Theory

Author: William Menasco

Publisher: Elsevier

Published: 2005-08-02

Total Pages: 502

ISBN-13: 9780080459547

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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

Applications of Knot Theory
Applications of Knot Theory

Author: American Mathematical Society. Short Course

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 203

ISBN-13: 0821844660

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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.

Topics in Knot Theory
Topics in Knot Theory

Author: M.E. Bozhüyük

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 355

ISBN-13: 9401116954

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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.