Knots And Links

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Knots and Links

Dale Rolfsen
Knots and Links Book PDF

Author : Dale Rolfsen
Publisher : American Mathematical Soc.
Page : 458 pages
File Size : 45,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9780821834367

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Knots and Links by Dale Rolfsen Pdf

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.""

Grid Homology for Knots and Links

Peter S. Ozsváth,András I. Stipsicz,Zoltán Szabó
Grid Homology for Knots and Links Book PDF

Author : Peter S. Ozsváth,András I. Stipsicz,Zoltán Szabó
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 45,6 Mb
Release : 2015-12-04
Category : Homology theory
ISBN : 9781470417376

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Grid Homology for Knots and Links by Peter S. Ozsváth,András I. Stipsicz,Zoltán Szabó Pdf

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 and Links

Peter R. Cromwell
Knots and Links Book PDF

Author : Peter R. Cromwell
Publisher : Cambridge University Press
Page : 346 pages
File Size : 52,5 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 0521839475

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Knots and Links by Peter R. Cromwell Pdf

Knot theory is the study of embeddings of circles in space. Peter Cromwell has written a textbook on knot theory designed for use in advanced undergraduate or beginning graduate-level courses. The exposition is detailed and careful yet engaging and full of motivation. Numerous examples and exercises serve to help students through the material, while an instructor's manual is available online.

An Introduction to Knot Theory

W.B.Raymond Lickorish
An Introduction to Knot Theory Book PDF

Author : W.B.Raymond Lickorish
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206910

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An Introduction to Knot Theory by W.B.Raymond Lickorish Pdf

A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant results are achieved and each chapter ends with exercises and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area.

The Knot Book

Colin Conrad Adams
The Knot Book Book PDF

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 41,9 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.

Knots, Links, Braids and 3-Manifolds

Viktor Vasilʹevich Prasolov,Alekseĭ Bronislavovich Sosinskiĭ
Knots Links Braids and 3 Manifolds Book PDF

Author : Viktor Vasilʹevich Prasolov,Alekseĭ Bronislavovich Sosinskiĭ
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 52,6 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821808986

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Knots, Links, Braids and 3-Manifolds by Viktor Vasilʹevich Prasolov,Alekseĭ Bronislavovich Sosinskiĭ Pdf

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.

A Gentle Introduction To Knots, Links And Braids

Ruben Aldrovandi,Roldao Da Rocha Jr
A Gentle Introduction To Knots Links And Braids Book PDF

Author : Ruben Aldrovandi,Roldao Da Rocha Jr
Publisher : World Scientific
Page : 214 pages
File Size : 40,6 Mb
Release : 2021-10-14
Category : Science
ISBN : 9789811248504

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A Gentle Introduction To Knots, Links And Braids by Ruben Aldrovandi,Roldao Da Rocha Jr Pdf

The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.

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 : 54,9 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.

Knots and Primes

Masanori Morishita
Knots and Primes Book PDF

Author : Masanori Morishita
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 49,9 Mb
Release : 2011-11-27
Category : Mathematics
ISBN : 9781447121589

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Knots and Primes by Masanori Morishita Pdf

This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory. Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry. ​

An Interactive Introduction to Knot Theory

Inga Johnson,Allison K. Henrich
An Interactive Introduction to Knot Theory Book PDF

Author : Inga Johnson,Allison K. Henrich
Publisher : Courier Dover Publications
Page : 192 pages
File Size : 50,5 Mb
Release : 2017-01-04
Category : Mathematics
ISBN : 9780486818740

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An Interactive Introduction to Knot Theory by Inga Johnson,Allison K. Henrich Pdf

This well-written and engaging volume, intended for undergraduates, introduces knot theory, an area of growing interest in contemporary mathematics. The hands-on approach features many exercises to be completed by readers. Prerequisites are only a basic familiarity with linear algebra and a willingness to explore the subject in a hands-on manner. The opening chapter offers activities that explore the world of knots and links — including games with knots — and invites the reader to generate their own questions in knot theory. Subsequent chapters guide the reader to discover the formal definition of a knot, families of knots and links, and various knot notations. Additional topics include combinatorial knot invariants, knot polynomials, unknotting operations, and virtual knots.

Formal Knot Theory

Louis H. Kauffman
Formal Knot Theory Book PDF

Author : Louis H. Kauffman
Publisher : Courier Corporation
Page : 274 pages
File Size : 55,6 Mb
Release : 2006-01-01
Category : Mathematics
ISBN : 9780486450520

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Formal Knot Theory by Louis H. Kauffman Pdf

This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author, Louis H. Kauffman, is a professor in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago. Kauffman draws upon his work as a topologist to illustrate the relationships between knot theory and statistical mechanics, quantum theory, and algebra, as well as the role of knot theory in combinatorics. Featured topics include state, trails, and the clock theorem; state polynomials and the duality conjecture; knots and links; axiomatic link calculations; spanning surfaces; the genus of alternative links; and ribbon knots and the Arf invariant. Key concepts are related in easy-to-remember terms, and numerous helpful diagrams appear throughout the text. The author has provided a new supplement, entitled "Remarks on Formal Knot Theory," as well as his article, "New Invariants in the Theory of Knots," first published in The American Mathematical Monthly, March 1988.

Quandles

Mohamed Elhamdadi, Sam Nelson
Quandles Book PDF

Author : Mohamed Elhamdadi, Sam Nelson
Publisher : American Mathematical Soc.
Page : 245 pages
File Size : 54,7 Mb
Release : 2015-08-27
Category : Knot theory
ISBN : 9781470422134

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Quandles by Mohamed Elhamdadi, Sam Nelson Pdf

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.

Knots and Links in Three-Dimensional Flows

Robert W. Ghrist,Philip J. Holmes,Michael C. Sullivan
Knots and Links in Three Dimensional Flows Book PDF

Author : Robert W. Ghrist,Philip J. Holmes,Michael C. Sullivan
Publisher : Springer
Page : 218 pages
File Size : 43,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540683476

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Knots and Links in Three-Dimensional Flows by Robert W. Ghrist,Philip J. Holmes,Michael C. Sullivan Pdf

The closed orbits of three-dimensional flows form knots and links. This book develops the tools - template theory and symbolic dynamics - needed for studying knotted orbits. This theory is applied to the problems of understanding local and global bifurcations, as well as the embedding data of orbits in Morse-smale, Smale, and integrable Hamiltonian flows. The necesssary background theory is sketched; however, some familiarity with low-dimensional topology and differential equations is assumed.

Hyperbolic Knot Theory

Jessica S. Purcell
Hyperbolic Knot Theory Book PDF

Author : Jessica S. Purcell
Publisher : American Mathematical Soc.
Page : 369 pages
File Size : 46,5 Mb
Release : 2020-10-06
Category : Education
ISBN : 9781470454999

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Hyperbolic Knot Theory by Jessica S. Purcell Pdf

This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of Mostow and Prasad with Gordon and Luecke, it was known that a hyperbolic structure on a knot complement in the 3-sphere gives a complete knot invariant. However, it remains a difficult problem to relate the hyperbolic geometry of a knot to other invariants arising from knot theory. In particular, it is difficult to determine hyperbolic geometric information from a knot diagram, which is classically used to describe a knot. This textbook provides background on these problems, and tools to determine hyperbolic information on knots. It also includes results and state-of-the art techniques on hyperbolic geometry and knot theory to date. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises. The level is appropriate for graduate students with a basic background in algebraic topology, particularly fundamental groups and covering spaces. Some experience with some differential topology and Riemannian geometry will also be helpful.

Surface-Knots in 4-Space

Seiichi Kamada
Surface Knots in 4 Space Book PDF

Author : Seiichi Kamada
Publisher : Springer
Page : 212 pages
File Size : 49,7 Mb
Release : 2017-03-28
Category : Mathematics
ISBN : 9789811040917

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Surface-Knots in 4-Space by Seiichi Kamada Pdf

This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.Knot theory is one of the most active research fields in modern mathematics. Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are related to braids and 3-manifolds. These notions are generalized into higher dimensions. Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surface-knot theory treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example, knot concordance and knot cobordism, which are also important objects in knot theory, are surfaces in the product space of the 3-sphere and the interval.Included in this book are basics of surface-knots and the related topics of classical knots, the motion picture method, surface diagrams, handle surgeries, ribbon surface-knots, spinning construction, knot concordance and 4-genus, quandles and their homology theory, and two-dimensional braids.