Knots Groups And 3 Manifolds

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Knots, Groups and 3-Manifolds (AM-84), Volume 84

Lee Paul Neuwirth
Knots Groups and 3 Manifolds AM 84 Volume 84 Book PDF

Author : Lee Paul Neuwirth
Publisher : Princeton University Press
Page : 346 pages
File Size : 42,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881512

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Knots, Groups and 3-Manifolds (AM-84), Volume 84 by Lee Paul Neuwirth Pdf

There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers are dedicated to the memory of Ralph H. Fox, one of the world's leading topologists, by colleagues, former students, and friends. In knot theory, papers have been contributed by Goldsmith, Levine, Lomonaco, Perko, Trotter, and Whitten. Of these several are devoted to the study of branched covering spaces over knots and links, while others utilize the braid groups of Artin. Cossey and Smythe, Stallings, and Strasser address themselves to group theory. In his contribution Stallings describes the calculation of the groups In/In+1 where I is the augmentation ideal in a group ring RG. As a consequence, one has for each k an example of a k-generator l-relator group with no free homomorphs. In the third part, papers by Birman, Cappell, Milnor, Montesinos, Papakyriakopoulos, and Shalen comprise the treatment of 3-manifolds. Milnor gives, besides important new results, an exposition of certain aspects of our current knowledge regarding the 3- dimensional Brieskorn manifolds.

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 : 46,6 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.

Quantum Invariants of Knots and 3-Manifolds

Vladimir G. Turaev
Quantum Invariants of Knots and 3 Manifolds Book PDF

Author : Vladimir G. Turaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 608 pages
File Size : 43,5 Mb
Release : 2016-07-11
Category : Mathematics
ISBN : 9783110435221

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Quantum Invariants of Knots and 3-Manifolds by Vladimir G. Turaev Pdf

Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups.The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space.This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents:Invariants of graphs in Euclidean 3-space and of closed 3-manifoldsFoundations of topological quantum field theoryThree-dimensional topological quantum field theoryTwo-dimensional modular functors6j-symbolsSimplicial state sums on 3-manifoldsShadows of manifolds and state sums on shadowsConstructions of modular categories

Introduction to 3-Manifolds

Jennifer Schultens
Introduction to 3 Manifolds Book PDF

Author : Jennifer Schultens
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 47,9 Mb
Release : 2014-05-21
Category : Mathematics
ISBN : 9781470410209

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Introduction to 3-Manifolds by Jennifer Schultens Pdf

This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex. With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.

Quantum Invariants

Tomotada Ohtsuki
Quantum Invariants Book PDF

Author : Tomotada Ohtsuki
Publisher : World Scientific
Page : 516 pages
File Size : 42,9 Mb
Release : 2002
Category : Invariants
ISBN : 9812811176

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Quantum Invariants by Tomotada Ohtsuki Pdf

This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The ChernOCoSimons field theory and the WessOCoZuminoOCoWitten model are described as the physical background of the invariants. Contents: Knots and Polynomial Invariants; Braids and Representations of the Braid Groups; Operator Invariants of Tangles via Sliced Diagrams; Ribbon Hopf Algebras and Invariants of Links; Monodromy Representations of the Braid Groups Derived from the KnizhnikOCoZamolodchikov Equation; The Kontsevich Invariant; Vassiliev Invariants; Quantum Invariants of 3-Manifolds; Perturbative Invariants of Knots and 3-Manifolds; The LMO Invariant; Finite Type Invariants of Integral Homology 3-Spheres. Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics."

Quantum Invariants of Knots and 3-Manifolds

Vladimir G. Turaev
Quantum Invariants of Knots and 3 Manifolds Book PDF

Author : Vladimir G. Turaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 600 pages
File Size : 44,8 Mb
Release : 2020-03-23
Category : Mathematics
ISBN : 9783110883275

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Quantum Invariants of Knots and 3-Manifolds by Vladimir G. Turaev Pdf

This monograph provides a systematic treatment of topological quantum field theories (TQFT's) in three dimensions, inspired by the discovery of the Jones polynomial of knots, the Witten-Chern-Simons field theory, and the theory of quantum groups. The author, one of the leading experts in the subject, gives a rigorous and self-contained exposition of new fundamental algebraic and topological concepts that emerged in this theory. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFT's and 2-dimensional modular functors from so-called modular categories. This gives new knot and 3-manifold invariants as well as linear representations of the mapping class groups of surfaces. In Part II the machinery of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFT's constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and Kauffman's skein modules. This book is accessible to graduate students in mathematics and physics with a knowledge of basic algebra and topology. It will be an indispensable source for everyone who wishes to enter the forefront of this rapidly growing and fascinating area at the borderline of mathematics and physics. Most of the results and techniques presented here appear in book form for the first time.

Knots and Links

Dale Rolfsen
Knots and Links Book PDF

Author : Dale Rolfsen
Publisher : American Mathematical Soc.
Page : 458 pages
File Size : 43,9 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.""

2-Knots and Their Groups

Jonathan Hillman
2 Knots and Their Groups Book PDF

Author : Jonathan Hillman
Publisher : CUP Archive
Page : 180 pages
File Size : 43,9 Mb
Release : 1989-03-30
Category : Mathematics
ISBN : 0521378125

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2-Knots and Their Groups by Jonathan Hillman Pdf

To attack certain problems in 4-dimensional knot theory the author draws on a variety of techniques, focusing on knots in S^T4, whose fundamental groups contain abelian normal subgroups. Their class contains the most geometrically appealing and best understood examples. Moreover, it is possible to apply work in algebraic methods to these problems. Work in four-dimensional topology is applied in later chapters to the problem of classifying 2-knots.

Knot Groups

Lee Paul Neuwirth
Knot Groups Book PDF

Author : Lee Paul Neuwirth
Publisher : Princeton University Press
Page : 124 pages
File Size : 52,9 Mb
Release : 1965-03-21
Category : Mathematics
ISBN : 0691079919

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Knot Groups by Lee Paul Neuwirth Pdf

The description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56, will be forthcoming.

3-manifold Groups

Matthias Aschenbrenner,Stefan Friedl,Henry Wilton
3 manifold Groups Book PDF

Author : Matthias Aschenbrenner,Stefan Friedl,Henry Wilton
Publisher : Erich Schmidt Verlag GmbH & Co. KG
Page : 236 pages
File Size : 44,5 Mb
Release : 2015
Category : Fundamental groups (Mathematics)
ISBN : 3037191546

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3-manifold Groups by Matthias Aschenbrenner,Stefan Friedl,Henry Wilton Pdf

The field of 3-manifold topology has made great strides forward since 1982 when Thurston articulated his influential list of questions. Primary among these is Perelman's proof of the Geometrization Conjecture, but other highlights include the Tameness Theorem of Agol and Calegari-Gabai, the Surface Subgroup Theorem of Kahn-Markovic, the work of Wise and others on special cube complexes, and, finally, Agol's proof of the Virtual Haken Conjecture. This book summarizes all these developments and provides an exhaustive account of the current state of the art of 3-manifold topology, especially focusing on the consequences for fundamental groups of 3-manifolds. As the first book on 3-manifold topology that incorporates the exciting progress of the last two decades, it will be an invaluable resource for researchers in the field who need a reference for these developments. It also gives a fast-paced introduction to this material. Although some familiarity with the fundamental group is recommended, little other previous knowledge is assumed, and the book is accessible to graduate students. The book closes with an extensive list of open questions which will also be of interest to graduate students and established researchers.

Knots and Primes

Masanori Morishita
Knots and Primes Book PDF

Author : Masanori Morishita
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 47,6 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. ​

New Ideas In Low Dimensional Topology

Vassily Olegovich Manturov,Louis H Kauffman
New Ideas In Low Dimensional Topology Book PDF

Author : Vassily Olegovich Manturov,Louis H Kauffman
Publisher : World Scientific
Page : 540 pages
File Size : 44,8 Mb
Release : 2015-01-27
Category : Mathematics
ISBN : 9789814630634

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New Ideas In Low Dimensional Topology by Vassily Olegovich Manturov,Louis H Kauffman Pdf

This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.

Knots

Gerhard Burde,Heiner Zieschang,Michael Heusener
Knots Book PDF

Author : Gerhard Burde,Heiner Zieschang,Michael Heusener
Publisher : Walter de Gruyter
Page : 432 pages
File Size : 43,5 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9783110270785

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Knots by Gerhard Burde,Heiner Zieschang,Michael Heusener Pdf

This 3. edition is an introduction to classical knot theory. It contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known.

A Survey of Knot Theory

Akio Kawauchi
A Survey of Knot Theory Book PDF

Author : Akio Kawauchi
Publisher : Birkhäuser
Page : 431 pages
File Size : 51,5 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.

Geometry and Topology

Mccrory
Geometry and Topology Book PDF

Author : Mccrory
Publisher : CRC Press
Page : 366 pages
File Size : 41,7 Mb
Release : 2020-12-17
Category : Mathematics
ISBN : 9781000110845

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Geometry and Topology by Mccrory Pdf

This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.