An Index Of A Graph With Applications To Knot Theory

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Index of a Graph with Applications to Knot Theory

Kunio Murasugi
Index of a Graph with Applications to Knot Theory Book PDF

Author : Kunio Murasugi
Publisher : Oxford University Press, USA
Page : 118 pages
File Size : 54,7 Mb
Release : 2014-08-31
Category : MATHEMATICS
ISBN : 1470400855

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Index of a Graph with Applications to Knot Theory by Kunio Murasugi Pdf

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.

An Index of a Graph with Applications to Knot Theory

Kunio Murasugi,Józef Przytycki
An Index of a Graph with Applications to Knot Theory Book PDF

Author : Kunio Murasugi,Józef Przytycki
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 41,6 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825709

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An Index of a Graph with Applications to Knot Theory by Kunio Murasugi,Józef Przytycki Pdf

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

Kunio Murasugi
Knot Theory and Its Applications Book PDF

Author : Kunio Murasugi
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 48,8 Mb
Release : 2009-12-29
Category : Mathematics
ISBN : 9780817647193

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Knot Theory and Its Applications by Kunio Murasugi Pdf

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.

Knot Theory and Its Applications

Krishnendu Gongopadhyay,Rama Mishra
Knot Theory and Its Applications Book PDF

Author : Krishnendu Gongopadhyay,Rama Mishra
Publisher : American Mathematical Soc.
Page : 357 pages
File Size : 52,5 Mb
Release : 2016-09-21
Category : Knot theory
ISBN : 9781470422578

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Knot Theory and Its Applications by Krishnendu Gongopadhyay,Rama Mishra Pdf

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

Akio Kawauchi
A Survey of Knot Theory Book PDF

Author : Akio Kawauchi
Publisher : Birkhäuser
Page : 431 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892278

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A Survey of Knot Theory by Akio Kawauchi Pdf

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.

Topics in Knot Theory

M.E. Bozhüyük
Topics in Knot Theory Book PDF

Author : M.E. Bozhüyük
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401116954

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Topics in Knot Theory by M.E. Bozhüyük Pdf

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.

Graph Structure Theory

Neil Robertson,Paul D. Seymour
Graph Structure Theory Book PDF

Author : Neil Robertson,Paul D. Seymour
Publisher : American Mathematical Soc.
Page : 706 pages
File Size : 43,9 Mb
Release : 1993-06-14
Category : Mathematics
ISBN : 9780821851609

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Graph Structure Theory by Neil Robertson,Paul D. Seymour Pdf

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.

Diagram Genus, Generators, and Applications

Alexander Stoimenow
Diagram Genus Generators and Applications Book PDF

Author : Alexander Stoimenow
Publisher : CRC Press
Page : 192 pages
File Size : 46,9 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781315362199

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Diagram Genus, Generators, and Applications by Alexander Stoimenow Pdf

In knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns ("generators"). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems. The book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators using Hirasawa’s algorithm and extends this description to push the compilation of knot generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of the genus 4 classification, including the braid index, polynomial invariants, hyperbolic volume, and Vassiliev invariants. The final chapter presents further research related to generators, which helps readers see applications of generators in a broader context.

Applications of Knot Theory

American Mathematical Society. Short Course
Applications of Knot Theory Book PDF

Author : American Mathematical Society. Short Course
Publisher : American Mathematical Soc.
Page : 203 pages
File Size : 51,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821844663

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Applications of Knot Theory by American Mathematical Society. Short Course Pdf

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.

Algebraic Topology. Poznan 1989

Stefan Jackowski,Bob Oliver,Krzysztof Pawalowski
Algebraic Topology Poznan 1989 Book PDF

Author : Stefan Jackowski,Bob Oliver,Krzysztof Pawalowski
Publisher : Springer
Page : 404 pages
File Size : 52,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540474036

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Algebraic Topology. Poznan 1989 by Stefan Jackowski,Bob Oliver,Krzysztof Pawalowski Pdf

As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.

Knots 90

Akio Kawauchi
Knots 90 Book PDF

Author : Akio Kawauchi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 652 pages
File Size : 46,8 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9783110875911

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Knots 90 by Akio Kawauchi Pdf

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Properties of Closed 3-Braids and Braid Representations of Links

Alexander Stoimenow
Properties of Closed 3 Braids and Braid Representations of Links Book PDF

Author : Alexander Stoimenow
Publisher : Springer
Page : 110 pages
File Size : 55,7 Mb
Release : 2017-11-29
Category : Mathematics
ISBN : 9783319681498

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Properties of Closed 3-Braids and Braid Representations of Links by Alexander Stoimenow Pdf

This book studies diverse aspects of braid representations via knots and links. Complete classification results are illustrated for several properties through Xu’s normal 3-braid form and the Hecke algebra representation theory of link polynomials developed by Jones. Topological link types are identified within closures of 3-braids which have a given Alexander or Jones polynomial. Further classifications of knots and links arising by the closure of 3-braids are given, and new results about 4-braids are part of the work. Written with knot theorists, topologists,and graduate students in mind, this book features the identification and analysis of effective techniques for diagrammatic examples with unexpected properties.

Unraveling the Integral Knot Concordance Group

Neal W. Stoltzfus
Unraveling the Integral Knot Concordance Group Book PDF

Author : Neal W. Stoltzfus
Publisher : American Mathematical Soc.
Page : 91 pages
File Size : 45,5 Mb
Release : 1977
Category : Mathematics
ISBN : 9780821821923

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Unraveling the Integral Knot Concordance Group by Neal W. Stoltzfus Pdf

The group of concordance classes of high dimensional homotopy spheres knotted in codimension two in the standard sphere has an intricate algebraic structure which this paper unravels. The first level of invariants is given by the classical Alexander polynomial. By means of a transfer construction, the integral Seifert matrices of knots whose Alexander polynomial is a power of a fixed irreducible polynomial are related to forms with the appropriate Hermitian symmetry on torsion free modules over an order in the algebraic number field determined by the Alexander polynomial. This group is then explicitly computed in terms of standard arithmetic invariants. In the symmetric case, this computation shows there are no elements of order four with an irreducible Alexander polynomial. Furthermore, the order is not necessarily Dedekind and non-projective modules can occur. The second level of invariants is given by constructing an exact sequence relating the global concordance group to the individual pieces described above. The integral concordance group is then computed by a localization exact sequence relating it to the rational group computed by J. Levine and a group of torsion linking forms.

The Index Theorem for Minimal Surfaces of Higher Genus

Friedrich Tomi,Anthony Tromba
The Index Theorem for Minimal Surfaces of Higher Genus Book PDF

Author : Friedrich Tomi,Anthony Tromba
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 50,7 Mb
Release : 1995
Category : Index theorems
ISBN : 9780821803523

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The Index Theorem for Minimal Surfaces of Higher Genus by Friedrich Tomi,Anthony Tromba Pdf

In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.

The Knot Book

Colin Conrad Adams
The Knot Book Book PDF

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 43,7 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821836781

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The Knot Book by Colin Conrad Adams Pdf

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.